Preheat your oven to 400°F. Set up two shallow bowls: one with flour seasoned with salt and pepper, and one with the Parmesan and panko mixed together until evenly combined.

Pat the chicken breasts dry with a paper towel, then season both sides with salt and pepper. Dredge each piece in the flour and shake off the excess, then press firmly into the Parmesan-panko mixture to coat well on both sides. Set aside on a clean plate.

Heat 2 tablespoons olive oil and 2 tablespoons butter in an oven-safe skillet over medium-high heat. Once the butter foams and the pan is hot, add the chicken breasts. Sear for about 3 minutes per side until deeply golden brown. Do not move the chicken while searing or the crust will break.

Transfer the skillet directly to the preheated oven and bake for 12 to 15 minutes, until the internal temperature reaches 165°F and the crust is crispy and golden all over. If the crust browns too fast, tent loosely with foil.

While the chicken bakes, melt the remaining 1 tablespoon of butter in a small saucepan over medium heat. Add minced garlic and cook for about 1 minute, stirring constantly, until fragrant. Do not let it brown.

Pour in the heavy cream and bring to a gentle simmer. Stir occasionally and let thicken for 3 to 4 minutes. Season with salt and pepper to taste. Optionally stir in a small handful of freshly grated Parmesan for extra richness.

Remove chicken from the oven and let rest for 3 minutes before plating. Spoon the creamy garlic sauce generously over the top, sprinkle with fresh parsley, and serve immediately.