Preheat oven to 400øF. Make enough pie enough to roll into 12 6"x6" squares (about a double batch.) Sprinkle each square with 1 tsp grated cheddar. Peel and core apples and place one on each square.
Fill the center of each apple with 2 tsp (or 1 heaping tsp) of mincemeat, 1 tsp of rum, a dot of butter and 1 Tablespoon sugar. Bring diagonally opposite corners of dough over the apple to form ears at the top. Cover the 'ears' with aluminum foil.
Mix the brown sugar, cream and grated lemon rind. Brush the dumplings with this mixture and bake 35 to 45 minutes in 400øF oven. Remove foil, brush ears with cream mixture and return to oven till 'ears' are brown. Serve warm to plain cream or sweetened cream, flavored with rum.