Grind the ham and fat fairly fine, either in a food processor or, in two batches, in an electric blender.
If using a processor, add the remaining ingredients at once and process until the mixture is rather like a coarse pate. If using a blender, scrape the first batch of ground ham into a bowl, add the seasonings, process the rest of the ham, and combine with the mixture in the bowl. If too coarse, process again in two batches.
Taste for seasoning, then pack into a jar, cover, and refrigerate overnight or longer to let the falvors mingle. The spread will keep for up to 2 weeks.
Makes about 1 1/2 cups