I had a dish similar to this in a small restaurant in Mexico, and at Gloria’s request, I created my own version at home. I use medium-size raw shrimp and puree the tails in a food processor, then combine the puree with pieces of the shrimp to form thick burgers.
1 ¼ pounds shelled and deveined medium shrimp
3 tablespoons chopped fresh chives
2 tablespoons olive oil
2 firm zucchini (about 1 pound), cut into 3/8-inch slices (about 3 1/2 cups)
½ teaspoon salt
½ teaspoon freshly ground black pepper
2 tablespoons unsalted butter
Minced fresh chives
Cut the shrimp crosswise in half. Process the tail pieces into a puree in a food processor and transfer to a bowl.
Cut the remaining shrimp into 1/2-inch pieces and add them to the bowl. Add the chives and mix well. Divide the mixture into 4 equal parts and form each one into a burger about 1 inch thick. (These can be made a few hours ahead and refrigerated.)
When ready to cook, heat the oil in a large skillet. Add the zucchini with 1/4 teaspoon each of the salt and pepper and saute over high heat for 4 to 5 minutes.
Meanwhile, melt the butter in another large skillet with a lid. Sprinkle the remaining 1/4 teaspoon each salt and pepper on the shrimp patties and place them carefully in the hot butter. Cook for about 1 1/2 minutes over high heat, then gently turn the burgers over. Cover, reduce the heat to medium, and cook for 2 to 2 1/2 minutes, until the burgers are barely cooked through.
Arrange the zucchini on four warm plates. Place the shrimp burgers on top, sprinkle with the chives, and serve.