Preheat oven to 400°.
Place each chicken breast half between 2 sheets of heavy-duty plastic wrap; pound to 1/4-inch thickness using a meat mallet or rolling pin.
Sprinkle chicken evenly with salt, 1/4 teaspoon basil, and crushed red pepper.
Sprinkle each chicken breast half with 1 tablespoon minced bell pepper. Place 1 cheese stick lengthwise down center. Roll up jelly roll fashion. Brush rolls evenly with Italian dressing.
Combine paprika and breadcrumbs; dredge chicken breast rolls in breadcrumb mixture, turning to coat. Place on a baking sheet coated with cooking spray seam side down. Lightly coat chicken rolls with cooking spray. Sprinkle evenly with remaining basil.
Bake at 400° for 15 minutes or until done. Let stand 5 minutes before serving.