It’s the end of harvest season in Extremadura, an out-of-the-way region of western Spain, and most of the land’s famed peppers have been dried and ground into the smoked paprika known as pimentón de la Vera.

I’d come to learn how locals use the aromatic spice and quickly found it in nearly everything—a bold single-­stroke solution to elevate everyday food. Mixed with fried breadcrumbs and leftover ham. Sprinkled over scrambled eggs. Stirred into boiled potatoes with olive oil.

But at Palacio Carvajal Girón, an elegant restaurant wrapped in the stone of a 16th-century palace, I’m reminded that pimentón also can be far more refined. Once a year, as part of an annual festival, the restaurant hosts a tasting menu: five plates, each featuring smoked paprika in some form.

It’s gelled into smoky pearls to garnish crispy nuggets of fried lamb. It’s dusted on surimi, a Japanese processed fish that resembles baby eels. Even dessert, an orange-spiked olive oil cake, is flecked with the spice.

Ironically, the standout dish at first appears to be the humblest: a simple crock of chickpeas. But here they’re embellished with chopped langoustines, whole shrimp and flakes of agri­dulce pimentón (a blend of sweet and spicy). Peeling the shrimp stains my fingers red, but it’s worth the trouble. Their sweet flesh balances the richness of tender beans and a smoky broth.

The dish’s apparent simplicity belies a complex recipe, says sous chef Miguel Angel Bernal, who grew up stomping through piles of dried peppers on his family farm nearby. Dry chickpeas are soaked overnight, then simmered with a ham bone. Separately, a shellfish broth is made with leeks, shrimp and sweet smoked paprika. In another pan, shrimp and langoustines are sautéed and chopped before everything is combined to simmer.

Back at Milk Street, we knew we needed an easier way to coax out that complexity. So we streamlined by cooking everything in a Dutch oven and using canned chickpeas and their starchy liquid to add body to the stew. We amped up the shellfish flavor with a cup of clam juice (making a separate broth unnecessary) and omitted langoustines altogether.

We first coated the shrimp in a mixture of sweet and spicy smoked paprikas. Searing the seasoned shrimp with the tails on created a flavorful crust, which we scraped up while sautéing the leeks, another nod to Bernal’s broth. Adding more of the paprika mixture later boosted the flavor while minimizing the heat’s dulling effect on the spice.

To prevent the shrimp from overcooking, we browned them on only one side. After removing the tails, we halved the shrimp and returned them to the finished chickpeas. They finished cooking in gentle residual heat. A quick simmer melded the flavors and mimicked the boldly rich dish we had in Spain, but with only one pot. And no messy fingers.