For the biscuits: Preheat the oven to 425 degrees F. Poke the sweet potatoes with the tines of a fork and bake until tender, about 1 hour. Let the potatoes cool, and then peel them, discarding the skins.
In a food processor, puree the potatoes with the buttermilk and nutmeg until smooth.
Whisk together the flour, sugar, baking soda and salt. With your fingertips or a dough cutter, cut in the cold butter until pea-size chunks are formed. Fold in the sweet potato puree until just combined, being careful not to overwork.
Dust a work surface with some flour and turn the biscuit dough onto the counter. Form the dough into a 3/4-inch-thick disc. Using a 2 1/4-inch round biscuit cutter, cut out 14 biscuits, starting on the outside of the disk and working your way in. You may need to reshape the last bits of dough back into a disk to get all 14 rounds.
Grease a 10-inch cast-iron skillet with the vegetable oil and place the biscuits in the skillet, working from the center out. The biscuits should be a tight fit and nestled against each other. Brush the biscuit tops with the melted butter and bake until golden, 15 to 18 minutes.
For the sandwich build: Split the hot biscuits, place some of the torn ham on the bottom half, drizzle the Blackberry Balsamic Drizzle over the ham and then pile some arugula on top for a peppery bite.
Blackberry Balsamic Drizzle:
Combine the preserves, basil, vinegar, mustard, peppercorns and chile in a medium saucepot on the stove. Set over medium heat. Simmer the sauce until thickened, 7 to 10 minutes. Strain the reduction through a fine sieve. Thin with water if needed.