The men are shrouded in a delicious, meaty smoke so thick it nearly obscures the massive stone arch and its flanking towers. Damascus Gate, one of the main entrances to the Old City of Jerusalem, has stood in some form and by various names for about 2,000 years. Throngs move in and out, the men calling out, announcing what the crowds already divine by smell alone.

They are about a dozen this day, and they are selling the city’s iconic street food, Jerusalem mixed grill, or meorav yerushalmi. The richness of the meats—some obviously chicken, some obviously random bits of this-and-that—is evident without tasting. Dripping and spiced, sopping with onions, all to be folded into pillowy pitas and drenched with tahini.

There is some dispute, of course, over who created the dish, but most agree it was a vendor in the city’s bustling Mahane Yehuda Market, a way to use up spare hearts, livers and spleens otherwise going to waste. Whatever the origins, the taste is indulgent and satisfying. I eat it standing amid the whirl of people, sizzle and history so strong it is palpable.

All of which is on my mind several years later when I slide onto a stool for lunch at the sleek U-shaped counter that wraps the open kitchen of the Barbary. It—along with sister eatery the Palomar—is part of a fresh wave of upscale London restaurants reimagining Israeli cooking. The food is bold, brash and punctuated with broad strokes of spice.

In Israel, mixed grill is a popular street food that uses up odd bits.

In Israel, mixed grill is a popular street food that uses up odd bits.

It is charred cauliflower splashed with tahini and pomegranate molasses. Whole scallions grilled and doused with labneh, sumac and oil. Salads of tomatoes, onions and riots of fresh herbs. Simple foods. Simply prepared. Wildly embellished. But it is head chef Daniel Alt’s take on Jerusalem mix—on the Barbary’s menu merely as J’ Mix—that grabs me most.

Chicken thighs seasoned with turmeric, coriander, cumin and cardamom, then seared on the grill. Pungent onions, creamy tahini and bright tomatoes complete it.

Dinner that evening is at the Palomar, where chef Omri McNabb offers a slightly different interpretation of the dish, his adding chili heat, the spark of citrusy sumac and the gentle sweetness of a touch of sugar.

Both are delicious. Both not merely recount my memories outside Damascus Gate, they improve on them in crave-worthy ways.