In a large skillet, heat 1/2 inch of canola oil to 350°.
Meanwhile, prepare three shallow bowls: In the first bowl, add the flour. In the second bowl, beat the eggs together. In the third bowl, mix the panko breadcrumbs with the oregano, basil, and grated cheese and season with salt and pepper.
Season the chicken with salt and pepper and dredge them in the flour; shaking off the excess. Dip the floured chicken thighs in the egg, allowing any excess to drip back into the bowl, then fully coat with the breadcrumb mixture.
Fry the cutlets in multiple batches until cooked through and browned, about 6 minutes per side. Transfer the cutlets to a rack set over a rimmed baking sheet.
Arrange the fried chicken in a 9x13 baking dish and top each with ⅛ cup marinara sauce followed by mozzarella and parmesan cheeses. Bake for about 25 minutes, or until browned and bubbling on top. Serve immediately.