Preheat the oven to 450°F (230°C). Pound chicken between sheets of heavy plastic to 1/2 in (1.3 cm) thick. Season thoroughly with salt and pepper.
Lightly and evenly dust both sides with flour. Beat eggs in a shallow bowl. In another bowl, combine panko with 1/2 cup (about 50 g) Parmesan.
Dip each floured breast in egg, then press into the panko mixture on both sides. Let the coated chicken rest for 10-15 minutes.
Heat about 1/2 in (1.3 cm) olive oil in a large skillet over medium-high heat until shimmering. Fry in batches without crowding, about 2 minutes per side, until golden. The chicken will finish in the oven.
Transfer chicken to a baking dish. Top each breast with 2 tbsp (30 mL) tomato sauce, then equal portions of mozzarella, basil, and provolone. Sprinkle with the remaining Parmesan and drizzle each breast with 1/2 tsp (2.5 mL) olive oil.
Bake 15-20 minutes, until the cheese is browned and bubbling and the chicken reaches at least 165°F (74°C). Rest briefly before serving.
Notes
Scaling: Allrecipes provides 1/2x and 2x ingredient controls but warns that times and steps do not automatically scale. Fry cutlets in batches and arrange them in a single layer in one or more baking dishes. Oven temperature remains 450°F (230°C).