Make the biscuits: Preheat oven to 450 degrees. In the bowl of a food processor, pulse dry ingredients to combine. Add butter and pulse several more times until butter pieces are about the size of small peas. Transfer mixture to a large bowl, add buttermilk, and stir with a fork (you can hold the fork stationary while spinning the bowl with your other hand) until a loose, shaggy dough begins to come together.
Turn dough out onto a clean, floured surface and roll to 1-inch thick. Cut dough into thirds, stack pieces, and re-roll to 1-inch thick. Cut biscuits into 2-inch squares, transfer to baking sheet, and brush tops with heavy cream. Bake for 15 to 18 minutes until biscuits are a light golden brown.
To assemble: When biscuits have cooled, halve and spread with mustard. Pile high with thinly sliced country ham and return tops to biscuits.