Preheat oven to 450°. Cut a slit down the side of each pepper to create a pocket; you don't need to seed peppers. Tuck some of the cheese into each pocket. Oil a medium, shallow baking dish with 2 tbsp. oil. Arrange peppers, cut side up, in a single layer.
Combine panko, paprika, and remaining 2 tbsp. oil. Season to taste with salt and pepper. Sprinkle mixture over stuffed peppers. Bake until panko browns and peppers soften, 10 to 20 minutes.