Preheat the oven to 375°F (190°C). Spray a 9x13-inch baking dish with nonstick spray.
Place the 4 raw boneless skinless chicken breasts in the prepared baking dish in a single layer; set aside.
In a mixing bowl, beat together 1 cup sour cream, 4 ounces softened cream cheese, 1/4 cup heavy cream, 2 tsp minced garlic, 2 tsp onion powder, 2 tsp garlic powder, 1/2 tsp dried thyme, 1/2 tsp dried rosemary, 1/2 tsp kosher salt, and 1/2 tsp ground black pepper with a hand mixer until smooth and well combined.
Spread the creamy herb mixture evenly over each chicken breast so they are fully coated.
Bake uncovered for 40–45 minutes, or until an instant-read thermometer inserted into the thickest part of the chicken reads 165°F (74°C).
Remove the dish from the oven, stir the sauce around the chicken to reincorporate any top crusted layer, and sprinkle with 1 tablespoon chopped fresh parsley.
Let the chicken rest briefly, then serve hot.