When I went to make my first ever version of Shrimp and Grits the other night, I sat down with a pen and paper and sketched out what I wanted it to look like, and listed the most desirable traits the dish could have. Yes, this is how I plan a meal. One of the ponderables was how to give the grits a subtle shrimpiness, so that the grits instead of being generic and suited to just about anything, no matter how good, seemed uniquely suited for the shrimp topping. I was only going to cook eight shrimp, four each, and the shells could provide a small amount of quick stock but that would also be needed for my sauce.
In Scott Peacock and Edna Lewis' delightful book Southern Cooking, I found my answer: puree a few extra cooked shrimp into some butter, along with sherry and cayenne pepper. If I had coral, which I did not, I would have added that too. Two tablespoons of that (effectively, one tablespoon per serving of grits) delivered the goods to a guilt-free "creamy" style grits made with half water and half 2% milk.
So I share:
1/2 pound raw shrimp, shells removed
1 tblsp butter AND 1 stick butter (1/4 lb) at room temp
1/4 cup dry sherry
1 tbslp lemon juice
pinch cayenne pepper or red pepper flakes
S & P to taste
Saute the shrimp in the 1 tblsp butter, allow to get a little golden color. Then blend with the rest of the ingredients in a food processor until a smooth paste is formed. Makes about 3/4 c. Keeps up to one week, but also freezes well.