Preheat oven to 400 degrees F. In a large skillet cook ground turkey, sweet pepper, and onion in hot oil over medium-high heat until turkey is brown, using a wooden spoon to break up turkey as it cooks. Stir in ketchup, mustard, pickle relish, and Worcestershire sauce.
Lightly press a biscuit onto the bottom and up the sides of each of ten 2 1/2-inch muffin cups. Divide turkey mixture among biscuit-lined muffin cups.
Bake for 9 minutes. Top with cheese. Bake about 5 minutes more or until cheese is melted. Cool in muffin cups on a wire rack for 5 minutes. Remove cheeseburger cups from muffin cups. If desired, garnish with dill pickle slices.