In a large skillet, melt 6 tablespoons of the butter until it foams. Add the shrimp and 1/2 teaspoon each of salt and black pepper. Cook over high heat, stirring, until the shrimp are pink and cooked through, about 5 minutes. Using a slotted spoon, transfer the shrimp to a food processor.
Return the skillet to high heat. Add the sherry, lemon juice and cayenne and cook until reduced to 3 tablespoons, 2 to 3 minutes. Pour the liquid over the shrimp and process until very smooth.
With the machine on, add the remaining butter, 1 tablespoon at a time, and process until smooth and silky. Transfer the shrimp paste to a serving bowl and let cool. Press a piece of plastic wrap directly onto the surface and refrigerated for at least 1 day. Bring to room temperature before serving.
The shrimp paste can be refrigerated for up to 1 week.