But it does no harm to the prime rib and the beef shoulder. They may not be great Texas-style barbecue, but they are still terrific slabs of roast beef, cooked medium-rare through and through and ringed with that salt-and-pepper crust. And the jalapeño-cheese links, shipped to Manhattan by Kreuz Market, are always full flavored and insistently spicy, though their juiciness varies from day to day.

When Hill Country opened, five years ago last month, it joined a wave of new restaurants that tried to coax more smoke into barbecue than had seemed possible on the tightly regulated shores of the East River. In a glowing $25 and Under column in 2007, the last time Hill Country was reviewed in The New York Times, Peter Meehan focused on the meat, especially the brisket. “No other barbecue place that has opened in New York in recent years has gotten it so right, right out of the gate,” he wrote.

Since then, Hill Country’s other virtues have become easier to notice, or harder to ignore. Year after year I am drawn back to the dessert case for another plastic cup of banana pudding, built upon a custard so thick with eggs and cream it brings Paris to mind, and not the one in Texas. And as New York has become cluttered with strenuously playful cupcakes, few make me smile as easily as the one at Hill Country that is filled with grape jelly and frosted with a fluffy turban of peanut butter.

According to hard-liners, the only permissible side dishes with barbecue are white bread and saltines. Anything else is as out of place as a yuzu macaron.

Hill Country takes a more liberal point of view, thankfully. When I can afford to surrender the stomach space, I will have some peppery corn pudding, which has roughly the same relationship to an ear of corn that an ice cream sundae has to a cow. And I am always grateful for the relief provided by crunchy, sparingly dressed coleslaw and a vinegary salad of black-eyed peas.

None of these dishes look like restaurant food; they seem like things packed for a church picnic by the best cook in town. The cook in this case, or at least the one whose recipes the kitchen follows, is the restaurant’s executive chef, Elizabeth Karmel. Named in her honor, EAK’s Bowl of Red is a ground-beef chili that could be a meal in itself, although it’s soupy enough that I wish Hill Country really did serve it in a bowl rather than in the same paper cartons used for all the sides.