Preheat the oven to 400°F (200°C) and grease a 13x9-inch baking dish with butter or cooking spray.
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 the dressing aside.
In a second shallow bowl, combine 1/2 cup Panko, 1/4 cup dry white bread crumbs, the remaining 2 tablespoons grated Parmesan, 1/8 tsp garlic powder, 1/8 tsp onion powder, and season with salt and pepper; mix well.
Dip each chicken breast into the basil-mayonnaise dressing, coating both sides evenly, then press into the breadcrumb mixture to coat both sides thoroughly.
Place the coated chicken breasts in a single layer in the prepared baking dish and spray the tops lightly and evenly with olive oil cooking spray.
Bake for 30–35 minutes until the chicken is cooked through and the coating is golden; if desired, broil for 1–2 minutes at the end to deepen browning, watching closely to avoid burning.
Remove from the oven and let rest briefly before serving warm.
