Preheat oven to 400 degrees F (200 degrees C). Grease a deep-dish pie plate.
Roll out biscuits, 1 at a time, into a thin rough 7-inch circles. Spread the center of each circle with 1 tablespoon cream cheese. Add 1 teaspoon cranberry sauce and 2 tablespoons each Swiss cheese, stuffing, and turkey. Bring dough up around the filling, pinching it together. Work your way around until the filling is fully encased in the biscuit bomb.
Place bombs on the pie plate, seam-side down. Repeat with remaining biscuits, cream cheese, cranberry sauce, Swiss cheese, stuffing, and turkey. Fit 7 bombs around the rim of the pie plate and 1 in the middle.
Brush melted butter over the top of each bomb. Sprinkle with salt and pepper.
Bake in the preheated oven, rotating once, until deep golden brown, 25 to 30 minutes.
Rest bombs on a cooling rack for 15 minutes before eating. Serve with warmed gravy for dipping.