The little hotel I found for my family of five was shockingly inexpensive thanks to its location in a peripheral neighborhood that one might describe as the Portage Park of Paris. While there weren’t any destination restaurants nearby, we did happen upon the local café. It was old and had seemingly seen better days before a tragic ’70s-era renovation. (You know the look: beveled mirrors, chrome accents, burnt sienna carpeting.) Yet it had a terrific covered patio, and the food was always on point. Added bonus: It never seemed to close.

So when Zach Engel, the chef-owner of Lincoln Park’s new Cafe Yaya, cited a trip to Paris with his wife and two young daughters as the restaurant’s inspiration, I knew exactly where he was going. “We have a weird idea in the States of what ‘café’ means,” he told me. “In Europe, it’s a place where you can go for a coffee and croissant at breakfast, have a light lunch, and then go back to for a full dinner. We didn’t feel like there was something here that encapsulated all that in Lincoln Park.”

When the long-abandoned space next to Galit, Engel’s lauded Middle Eastern restaurant, became available at a good price, he and business partner Andrés Clavero seized the opportunity. They opened Cafe Yaya in March, at first serving only breakfast, with coffee and pastries by Galit pastry chef Mary Eder-McClure. Then came a full dinner menu, followed by a more abbreviated lunch one. They began serving a few snackums in the late afternoon and finally debuted Sunday brunch in the upstairs dining room and event space. Voilà! All day.

I’ve been going … and going … and going. I’ve had everything from coffee and a pastry to a blowout dinner with cocktails and wine — seven meals total. I’ve tried to experience this place in all its moods and make sense of the mish-mosh menu that reflects Engel’s unique background: a rabbi’s son from the American South who’d make trips to Israel with his parents and became a cook in New Orleans, specializing in the Levantine cuisine of Palestine and Israel.

After all those meals, though, I still consider Cafe Yaya a work in progress. If you’re a fan of Engel’s cooking at Galit (many people, myself included, consider him one of Chicago’s best chefs) and want to try everything at his sophomore project, you’ll find it promising but uneven. Nonetheless, if you’re contemplating a spontaneous meal and Cafe Yaya pops into mind, go. The menu is all about meeting your appetite and hankerings, and becoming a place to rely on when flashier restaurants don’t appeal.

Unlike trendier all-day cafés that trade in algorithmically sanctioned minimalist calm and are powered by matcha and avocado toast, Cafe Yaya feels like it has been there forever. Engel’s twin sister, Ilana Engel, devised a logo that looks like a Roman mosaic, and Siren Betty Design ran with the theme, painting bucolic frescoes on the exposed brick and focusing the long, narrow room around three points: a wood-burning oven, a bar stocked with beverage director Scott Stroemer’s eclectic wines, and a pastry case displaying the day’s offerings.

Eder-McClure has a lot of fun bringing Middle Eastern flavors to savory pastries. Her za’atar twist tastes like a spice-dusted Palestinian flatbread collided with a Danish, and it’s something I could eat on the regular. Also great is her shakshuka bun, a crusty challah cup filled with seasoned tomatoes and a baked egg. You might find a lovable cardamom kouign-amann, all buttery layers and crisp sugary glaze, among the half-dozen options that rotate daily. Consider ordering a “breakfast sammie,” though my merguez sausage and egg version arrived cold in a too-big challah bun with tahini inexplicably on the side. Maybe you’ll have better luck.

That same element of chance appears when you crack open the dinner menu, which is a delightful document to explore but a hard one to figure out. As at Galit, dips, spreads, and bread take up a lot of real estate, but here it’s all à la carte and offbeat. There’s no hummus, but there is a caramelized onion and miso labneh (a fun take on the French onion trend), pimento cheese, and a sweet black garlic tahini. Now what do you dip with? A nice but boring basket of bread? A flaky Yemenite flatbread called malawach? Crackers? It’s a shame you can’t get an assortment of all, particularly when it’s two of you dining.

When my wife and I ate at the bar, we didn’t care for the dips as much as those next door, but the rest of the meal was spot on. We slurped perfectly iced oysters and split a pork schnitzel that kept its crunch under a heap of maitake mushrooms and parsley in a bright lemon sauce. Steak fries the size of ingots made for ideal sauce soppers. We also enjoyed chatting up the personable bartender and having a few tasters of wine before settling into our glasses: a white blend from Castel Pujol in Uruguay for her, and a skin-contact Pinot Grigio from Kobal in Slovenia for me.

I wish a big dinner with old friends had landed as well. Some dishes, like shrimp rémoulade with fried green tomatoes or grilled sweetbreads in caramelized onion gravy, were acidic enough to obliterate all other tastes. The mushroom-eggplant stew and a crock of collard greens with baked feta were unattractive and muddy. A wood-oven-roasted half chicken looked gorgeous but was dry to the bone. Nor did our round of cocktails impress; I’m never going to be on team tahini-washed vermouth.

And yet, this food is interesting, the service (counter during the day, full at night) is great, and I always want to go back. At lunchtime, a salad with perfect greens and (blessedly juicy) chicken shawarma wasn’t a gourmet revelation but just what my body and soul needed. And for an early-evening bite with a friend, we split a carafe of easygoing white, a tall lamb burger on a puffy challah bun with tangy, pickley condiments, and a basket of the best shoestring fries this side of Mickey D’s. At that moment I felt so grateful that Cafe Yaya exists, because there was no place I’d rather have been.