Preheat the oven to 425°F. Set a wire rack on a baking sheet and set aside. That rack is for the rest later — it keeps the bottom crust from steaming.
Pound each chicken breast between two sheets of plastic wrap to an even 1/2-inch thickness, focusing on the thick end.
In a small bowl, stir together the mayonnaise, Dijon, garlic powder, smoked paprika, and a pinch of salt and pepper until it looks like pale golden dressing.
In a shallow dish, toss the panko with the grated Parmesan and a generous grind of black pepper. Press the mixture between your fingers to roughen the panko — those craggy bits get extra crispy.
Pat each chicken breast dry with a paper towel. Spread the binder on both sides, then press the chicken into the crust mixture firmly with the heel of your hand. Do both sides and pat down any bare spots.
Place the coated chicken on the wire rack and refrigerate for 10 minutes while the oven finishes preheating. This helps the crumbs glue themselves to the binder.
Melt the butter or heat the oil in a 12-inch oven-safe skillet over medium-high heat. When it is shimmering and a test crumb sizzles steadily, lay in the chicken and sear 2 to 3 minutes per side until deep golden. Do not move the chicken around; let it release on its own.
If your skillet is oven-safe, leave the chicken in it; otherwise transfer to the prepared baking sheet. Bake for 12 to 14 minutes, until the crust is deep bronze at the edges and the kitchen smells nutty and sharp. The thickest part should reach 165°F.
Let the chicken rest on the rack for 5 minutes before cutting. The juices will settle back into the meat and the crust will stay crisp.