Place the sweet potatoes in a steamer and steam until very tender, about 12 minutes. Heat the oven to 375° and coat a standard 12-cup muffin tin with cooking spray.
In a large bowl, lightly beat the eggs. Add the carrot, parsnip, garlic, bread crumbs, tomato paste or ketchup, Worcestershire sauce, thyme, 1 teaspoon of the salt, and 1/4 teaspoon of the pepper and stir to combine. Mix in the pork. In a separate bowl, mash together the steamed sweet potatoes, flour, butter, nutmeg, and the remaining salt and pepper.
Evenly divide the pork mixture among the muffin wells. Spoon and spread the potato mixture over the top of each cup and scatter on the Parmesan. Bake the pies until a thermometer inserted into the meat in the center of one of the cupcakes registers 160°, about 20 minutes. Cool the cupcakes for 5 minutes before unmolding them.