Position a rack at the center of the oven and preheat to 375°.
Pat the chicken dry using paper towels.
In a blender or food processor, combine the oats, cheese, paprika, salt, and pepper and process for about 1 minute. Pour the mixture into a pie plate and one by one, dredge the chicken pieces in the oat mixture, dip them in the milk, and dredge them in the oat mixture again.
Place the chicken on a 15 x 10-inch jelly-roll pan or baking tray. Drizzle with butter and bake until the chicken is fork tender and cooked through, 55 minutes to 1 hour.