Make the marinara sauce: sauté the onion in olive oil for 5 minutes. Add the tomatoes and a handful of basil. Simmer uncovered for 15-20 minutes. Set aside.
Add the shredded zucchini to a bowl with 1 teaspoon salt; mix well. Squeeze excess liquid from zucchini. Add 1 cup mozzarella, garlic, and red pepper flakes; stir until combined.
Salt and pepper the chicken. Make an incision lengthwise in each chicken breast to form a pocket. Fill each chicken breast with about 1/4 cup of zucchini mixture. (Use a couple of toothpicks to hold the pocket closed.)
Mix the Parmesan and breadcrumbs in a medium bowl. Place the flour on a plate and season with salt and pepper. Place the beaten eggs in a large bowl. Dredge the chicken in flour, then egg, then breadcrumb mixture.
In a large pan, heat 1/2 inch of oil on medium-high heat. Fry the chicken breasts until golden brown.
Place chicken in a baking dish, top with marinara, mozzarella, and Parmesan. Cover with foil and bake for 15 minutes. Remove the foil and bake for an additional 15 minutes. Garnish with more Parmesan and chopped basil.