This Lowcountry version of shrimp paste relies on minimal ingredients, butter and shallots mainly, to retain the simplicity and flavor of the dish. Using a food processor means you can have it ready for cocktail hour in a snap.
Fit the bowl of the processor with a steel blade and put in the shrimp. Cover and pulse until coarsely ground.
Add the butter and shallots and process until the mixture forms a paste. Don't over-process it to a mousse consistency: there should still be some texture. Season to taste with salt, a liberal grinding of white pepper, and a pinch or so of cayenne. Pulse a few times to mix the seasonings. Taste and adjust the seasoning and pulse until mixed.
Lightly butter a 3-cup metal mold, or two smaller molds, or a small loaf pan. Press the paste firmly into it, making sure there are no pockets of trapped air. Cover with a plate or plastic wrap and chill for several hours until firm.
To unmold, stand the mold in a basin of hot water for 1 minute. Loosen the edges with a knife, and invert the mold over a serving plate—the shrimp paste should come out with a couple of firm taps on the top of the mold. Smooth any gaps with a spatula and let it stand until it's soft enough to spread. Serve with biscuits, toast points, or Melba toasts.