For the chicken: Cut each chicken breast in half, and then pound to a thickness of 1/2-inch.
Combine the buttermilk, hot sauce and salt in an 8-by-8-inch baking dish. Add the chicken and turn to coat. The chicken may be refrigerated for up to 24 hours before cooking.
For the dredge: On a rimmed baking sheet, mix the flour, salt, pepper, garlic powder, onion powder and dried thyme. Remove the chicken from the buttermilk bath and press into the flour mixture to thoroughly coat each side. Leave them in the flour while the oil heats.
Fill a large oval Dutch oven with oil to a depth of 2 inches and heat the oil to 325 degrees F. Grab each piece of chicken and slap it back and forth between your hands a few times to knock off the excess flour before slipping it into the oil. Cook until golden brown, flipping once halfway through, 4 to 6 minutes. Carefully transfer to a cooling rack and rest for a minimum of 2 minutes.
While still on the cooling rack, top each of the chicken breasts with an equal amount of marinara sauce, mozzarella and Parmesan. Place the chicken underneath a broiler to melt the cheese, watching carefully. When the cheese is melted, serve immediately.
The chicken may be refrigerated for up to 24 hours before cooking.