To make burgers, combine ground turkey, rolled oats, egg, salt, and pepper in a medium bowl and mix well. Form into 4 flat patties of equal size.
Grill over medium heat, flipping halfway through, until browned on the outside and cooked through. (*Top each with 2 oz. cheese immediately after flipping.)
Assemble burgers inside pretzel rolls by topping each with 2 Tbsp. chopped walnuts, 3 apple slices, 1/4 c. spinach leaves, and 3 Tbsp. apple butter.