Preheat the oven to 400°F (200°C) and butter or spray a 13x9-inch baking dish.
In a shallow bowl, whisk together 1/4 cup mayonnaise, 1/4 cup buttermilk, 1 1/2 tsp dried basil, 2 tablespoons of the grated Parmesan, 1/8 tsp garlic powder, and salt and pepper to taste; set aside.
In a second shallow bowl, combine 1/2 cup Panko, 1/4 cup dry white bread crumbs, the remaining 2 tablespoons Parmesan, 1/8 tsp onion powder, 1/8 tsp garlic powder, and salt and pepper to taste; mix until evenly combined.
Dip each chicken breast into the basil-mayo mixture to coat both sides, then press into the breadcrumb mixture to fully coat both sides. Repeat for all pieces and arrange in a single layer in the prepared baking dish.
Spray the tops of the coated chicken lightly and evenly with olive oil cooking spray.
Bake for 30–35 minutes, until the chicken is cooked through and the crust is golden. For extra browning, move the oven rack higher and broil for 30–60 seconds while watching closely to avoid burning.
Remove from the oven and let rest briefly before serving warm.