Preheat oven to 350 degrees F (175 degrees C). Line a rimmed baking sheet with parchment paper.
Make a V-shaped cut in each roll, leaving the ends intact. Lift out V-shaped wedge. Hollow out rolls gently to make shallow bread bowls, being careful not to cut through the bottom or sides. Place bread bowls on the prepared baking sheet.
Whisk eggs in a bowl. Add milk; whisk until well blended. Stir in green chile peppers, Cheddar cheese, pepper Jack cheese, paprika, and salt. Pour mixture slowly into the prepared rolls, spreading evenly with a spoon.
Bake in the preheated oven until egg mixture is completely set and cheese is lightly browned, about 30 minutes. Cool for 3 minutes before serving.