Finely chop pepper and onion, and grate carrot. Place 1/4 cup of each into a large bowl. Add egg white and bread crumbs; stir well to combine. Season with salt and pepper; stir in Parmesan cheese and turkey.
Mix by hand and shape into 4-6 patties according to your preferred size of burgers. Spray a skillet with cooking spray and heat over medium. Add burgers and cook for 5-6 minutes on each side or until no longer pink in the center.
Slice tomato. Serve each burger on a bun with a tomato slice and spinach leaves. Serve pineapple on the side.