Preheat the oven to 375°F (190°C) and spray a 9x13-inch baking pan with nonstick spray.
Place the raw chicken breasts in the prepared baking dish in a single layer; set aside.
In a mixing bowl, beat the sour cream, softened cream cheese, heavy cream, minced garlic, onion powder, garlic powder, dried thyme, dried rosemary, kosher salt, and black pepper with a hand mixer on high until smooth and well combined.
Spread the creamy herb mixture evenly over each chicken breast, covering the top.
Bake uncovered for 40–45 minutes, or until the internal temperature of the thickest breast reaches 165°F (74°C); check with an instant-read thermometer.
Remove from oven and gently stir the sauce around the chicken so the top layer blends into the rest of the sauce.
Sprinkle chopped fresh parsley over the chicken and serve hot.