Preheat the oven to 350 degree F. Line a rimmed baking sheet with parchment paper. Lay the chicken breasts flat on the baking sheet. Starting from one side, cut a deep slit (or pocket) into each chicken breast, parallel to the baking sheet, leaving three sides intact. Try to make the cut even so the attached edges are all about ½-inch thick.
Squeeze as much moisture out of the thawed spinach as possible. Then mix the spinach, shredded cheese, red peppers, shaved onion, garlic, paprika, and ¼ teaspoon salt together in a mix bowl.
Stuff the mixture evenly into the chicken breasts, turning them upright, so the stuffing is facing up. Drizzle each breast with olive oil and sprinkle generously with salt and pepper.
Bake for 25 minutes, until the cheese is bubbly and the chicken is cooked through at the thickest point. Serve warm!
