Put 1 of the chicken breasts between 2 large pieces of plastic wrap and use a meat tenderizer or rolling pin to lightly pound and flatten the chicken until it is a little less than 1/2-inch thick. Repeat with the second chicken breast. Set aside.
Put the flour, eggs and panko in 3 separate small baking dishes or shallow bowls and season each with salt and pepper. Add 2 tablespoons of the Parmesan and the Italian seasoning to the panko. Sprinkle the chicken on both sides with salt and pepper. One at a time, dredge each breast in the flour, dip in the egg and let excess drip back into the bowl, then coat with panko.
Add enough canola oil to a large skillet to come to a depth of 1/2 to 1 inch. Heat the oil between medium and medium-high heat until it starts to shimmer. Test the temperature of the oil by sprinkling several panko breadcrumbs into the oil; if the crumbs start to bubble immediately and quickly turn golden brown, the oil is ready for frying. Carefully add both chicken breasts to the oil and fry until golden brown and a thermometer inserted into the center of both of the breasts registers 165 degrees F, 4 to 5 minutes per side; use a clean spatula or tongs to flip the chicken.
Transfer the fried breasts to a cooling rack set over a baking sheet and season with a pinch of salt. Position an oven rack 5 to 6 inches from the broiler and preheat the broiler to high.
Spread 1/4 cup marinara sauce inside of a 2-quart flame-proof baking dish. Lay the ravioli in a single layer in the dish. Top with the chicken, then spoon the remaining 1 1/2 cups marinara evenly over the chicken and some of the ravioli. Sprinkle the chicken and ravioli with the mozzarella and the remaining 2 tablespoons Parmesan. Broil until the cheese is melted and browned on top, 3 to 5 minutes, depending on your broiler. Sprinkle with the parsley and serve immediately.