Preheat oven to 425°F (220°C). Line a large baking sheet with parchment paper.
Prepare potatoes: Toss halved potatoes with 2 tablespoons olive oil, ½ teaspoon salt, ¼ teaspoon pepper, and paprika.
Season chicken: Pat chicken dry, brush with remaining oil, and season with salt, pepper, and garlic powder.
Arrange on pan: Spread potatoes cut-side down in a single layer. Place chicken breasts among potatoes.
Initial bake: Bake for 20 minutes.
Make sauce: While baking, melt butter in a saucepan over medium heat. Add garlic and sauté 1-2 minutes. Add cream and bring to gentle simmer. Reduce heat to low and gradually whisk in 1 cup Parmesan until smooth. Add all seasonings and stir well.
First sauce application: After 20 minutes, remove pan from oven. Spoon half the sauce over chicken and potatoes.
Continue baking: Return to oven for 20-25 minutes until chicken reaches 165°F internal temperature and potatoes are golden.
Finish: Remove from oven, drizzle with remaining sauce, and sprinkle with reserved ¼ cup Parmesan and fresh parsley.
Rest and serve: Let chicken rest 5 minutes before serving.