To prepare the chicken breasts, make a horizontal cut through the thickest part of each breast, being careful not to slice all the way through. Open up the chicken breast like a book.
In a bowl, combine the cooked broccoli and shredded cheddar cheese. Spoon the mixture onto one side of each butterflied chicken breast, then fold it over on itself to make a stuffed chicken breast.
In a shallow dish, mix the breadcrumbs, grated Parmesan cheese, garlic powder, paprika, salt, and black pepper.
Take each stuffed chicken breast and dip it into the breadcrumb mixture, ensuring both sides are evenly coated. Gently press the breadcrumbs onto the chicken to help them adhere.
Prepare a baking sheet by lining it with parchment paper or greasing it lightly. Place the breaded chicken breasts onto the prepared baking sheet.
Drizzle a little olive oil over the top of each chicken breast to help the browning process.
Bake the chicken for approximately 25-30 minutes, or until the chicken is thoroughly cooked and the coating turns golden brown.