Heat 1/3 cup of the butter in a large skillet until melted. Add the shrimp, salt, and black pepper and cook over high heat, stirring often, until the shrimp are cooked through. This will take about 5-6 minutes.

Transfer the cooked shrimp to the bowl of a food processor fitted with a steel blade. Set aside.

In the same skillet, add the cooking wine, lemon juice, and cayenne pepper. Cook over high heat until the liquid is reduced to about 3 tablespoons and is quite syrupy.

Immediately add the mixture to the shrimp in the food processor and process until the shrimp are puréed. With the motor running, add the remaining butter, a few pieces at a time, and process until thoroughly blended. Turn the food processor off and taste the shrimp paste for seasoning. Add additional salt or black pepper as needed.

Let the shrimp paste cool completely before using. Store covered in the fridge for up to one week.