Heat oven to 400º F. Line a baking sheet with parchment.
Combine the Parmesan, paprika, and ¼ teaspoon salt in a small bowl.
Brush both sides of the pita cats with the butter. Sprinkle one side with the Parmesan mixture. Bake on the prepared pan until golden brown and crisp, 4 to 5 minutes. Serve warm or at room temperature.