Preheat your oven to 375°F (190°C). Lightly grease a 9×13-inch glass casserole dish and set it aside. (Glass is highly recommended here for even bubbling and heat distribution!).
Step 2: Season the Chicken
Pat the chicken breasts completely dry with paper towels. Sprinkle both sides with about ½ teaspoon of the salt and ¼ teaspoon of the black pepper. Lay the seasoned chicken breasts in a single layer in your prepared glass dish, leaving a little space between each piece so the sauce can flow around them.
Step 3: Mix the Silky Topper
In a medium mixing bowl, combine the crushed tomatoes, heavy cream, grated Parmesan, dried basil, minced garlic, red pepper flakes, olive oil (or melted butter), the remaining salt and pepper, and the sugar. Stir well until the mixture looks smooth and creamy.
Step 4: The Pour-Over
Crucial Step: Hold the bowl over the glass casserole dish and slowly pour this silky topper evenly over the raw chicken breasts. Make sure each piece of meat is well coated, and use a spoon to gently nudge the sauce into the corners of the dish so no chicken is left bare!
Step 5: The Covered Bake
Cover the glass casserole dish tightly with aluminum foil and place it on the middle rack of the preheated oven. Bake for 25 minutes to let the chicken gently poach in the creamy sauce.
Step 6: Uncover and Finish
After 25 minutes, carefully remove the foil (watch out for the hot steam!). Return the uncovered dish to the oven and bake for another 15 to 20 minutes, or until the chicken is cooked through to an internal temperature of 165°F (74°C). The sauce should be bubbling around the edges and slightly thickened.
Step 7: Rest and Serve