Sprinkle each side of cutlet with 1/8 teaspoon salt and let stand at room temperature for 20 minutes. Meanwhile, combine mozzarella and fontina in a bowl; set aside.
Adjust oven rack 4” from broiler element and heat broiler. Whisk egg and flour together in shallow dish until smooth.
In a second shallow dish, combine Parmesan, panko, garlic powder, oregano, and pepper. Pat chicken dry with paper towels.
Working with one cutlet at a time, dredge cutlet in egg mixture, allowing excess to drip off. Coat all sides in Parmesan mixture, pressing gently so crumbs adhere. Transfer cutlet to large plate and repeat with remaining cutlets.
Heat oil in a 10” nonstick skillet over medium-high heat until shimmering. Carefully place 2 cutlets in skillet and cook without moving them until bottoms are crispy and deep golden brown, 1 1/2 to 2 minutes.
Carefully flip cutlets and cook on second side until deep golden brown, 1 1/2 to 2 minutes. Transfer cutlets to paper-towel lined plate and repeat with remaining cutlets.
Place cutlets on rimmed baking sheet and sprinkle cheese mixture evenly over cutlets, covering as much surface area as possible. Broil until cheese is melted and beginning to brown, 2-4 minutes.
Transfer chicken to serving platter and top each cutlet with 2 tablespoons sauce. Sprinkle with basil and serve immediately over spaghetti, passing remaining sauce separately.