Make the sauce: Heat 1 tablespoon oil in a medium saucepan over medium heat. Add the minced garlic, 3/4 teaspoon salt, 1/4 teaspoon dried oregano, and red pepper flakes; cook, stirring, until fragrant, about 30 seconds to 1 minute.
Stir in the crushed tomatoes and bring to a simmer over medium-high heat. Reduce heat to medium-low and simmer gently about 20 minutes.
Remove the sauce from heat, stir in 2 tablespoons chopped fresh basil and the remaining 1 tablespoon oil, and adjust seasoning with salt and pepper to taste.
Prepare the chicken: Sprinkle each cutlet with about 1/8 teaspoon kosher salt and let sit at room temperature for 20 minutes.
Combine the shredded mozzarella and fontina in a small bowl and set aside.
In a shallow dish whisk the egg and 1 tablespoon flour until smooth. In a second shallow dish combine the grated Parmesan, panko, 1/2 teaspoon garlic powder, 1/4 teaspoon dried oregano, and 1/4 teaspoon black pepper.
Pat the chicken dry with paper towels. Dredge each cutlet in the egg-flour mixture, then press into the Parmesan-panko mixture to coat both sides, pressing gently so crumbs adhere. Set aside on a plate.
Heat the vegetable oil in a 10-inch nonstick skillet over medium-high heat until shimmering. Working two cutlets at a time, fry without moving until the bottoms are golden and crisp, about 1½–2 minutes. Flip and cook the second side until golden. Transfer to a paper towel–lined plate and repeat with remaining cutlets.
Place the fried cutlets on a baking sheet. Evenly sprinkle the mozzarella-fontina mixture over each cutlet.
Broil on high until the cheese melts and begins to brown, about 2–4 minutes; watch carefully to avoid burning.
Transfer to a serving platter, top each cutlet with a couple tablespoons of sauce and torn fresh basil, and serve immediately.