Melt the butter slowly on the stove, or melt it in the microwave. When it's melted, pour the clear part of the butter into a small bowl, trying to leave as many of the solids behind in the pan as possible. Just discard the solids. Let the butter cool a bit.
Put the ham, the seasonings and three-quarters of the butter into a food processor and whiz till you have a smooth paste. Adjust the taste.
Put into a container or bowl, and put enough of the remaining butter on top of it to make a thin layer of butter. Cover with plastic wrap, and refrigerate.
You can serve this after about 1/2 hour, but it's even better made a day ahead.This recipe is easily doubled or tripled.