Preheat the oven to 300 degrees F. Line a baking sheet with parchment and set aside.
Set up your dredging station. On a large plate, combine all the ingredients for the bread crumbs and stir to combine. Beat the egg in a shallow medium bowl. Set the dishes side by side. Working on piece at a time, dip the chicken first in the egg and allow the excess to drip back into the bowl. Then dip it in the bread crumbs, turning to coat and pressing to adhere.
In a large sauté pan, set over medium heat, add a few tablespoons of olive oil. When shimmering, add the first two piece of dredged chicken and cook on each side for about 3 to 4 minutes. Flip and cook on the opposite sides for about the same time, until lightly golden brown. When done, transfer to the baking sheet. Repeat with the remaining two chicken breasts.
Meanwhile, let's make the sauce. Heat a few tablespoons of oil in a large skillet over medium heat. When the oil is shimmering, add the onion, garlic, and red pepper flakes and cook for 2 minutes or until the onion begins to soften. Add the tomatoes with their juices and the oregano, and season with salt and pepper. Crush the tomatoes with the back of a wooden spoon. Reduce the heat to low and simmer for 10 minutes or until the sauce thickens. Stir in the basil. Transfer half the sauce to a medium bowl and set aside, reserving the remainder in the skillet over low heat.
Spoon a few tablespoons of sauce over the chicken breasts and then top each with a slice of mozzarella. Transfer to the oven until the cheese is all melty, about 5 minutes.
Return the skillet with the remaining sauce to medium-high heat. Add the zucchini noodles and cook for about 5 minutes or until al dente. Divide the noodles among four plates. Top with the chicken.