Preheat oven to 375°F (190°C).
In a shallow bowl, combine Parmesan cheese, breadcrumbs, minced garlic, salt, and black pepper.
Brush chicken breasts lightly with olive oil.
Dredge each chicken breast in the breadcrumb mixture pressing gently to coat evenly.
Heat butter and remaining olive oil in a large oven-safe skillet over medium heat.
Add chicken and cook until golden brown on both sides, about 3-4 minutes per side.
Transfer skillet to the oven and bake chicken for 12-15 minutes until cooked through.
Meanwhile, in a small saucepan, heat heavy cream over low heat until warm.
Stir in remaining Parmesan cheese until the sauce thickens slightly.
Remove chicken from oven, spoon Parmesan cream sauce over the top, and garnish with chopped parsley.
Serve immediately with sauce spooned generously over each chicken breast.