Preheat oven to 400°F (200°C) and grease a 9x13 inch baking dish.
Heat olive oil in a large skillet over medium-high heat. Season chicken with salt and pepper and sear until browned on all sides, approximately 5-7 minutes.
Blanch broccoli florets in boiling water for 2 minutes, then immediately drain and shock in cold water to preserve color and texture.
In a small saucepan, whisk together heavy cream, minced garlic, dried oregano, and red pepper flakes over medium heat. Simmer for 3-5 minutes until slightly thickened, then stir in Parmesan cheese.
Combine the seared chicken, blanched broccoli, and sun-dried tomatoes in the prepared baking dish.
Pour the cream sauce over the chicken and vegetables, tossing gently to coat evenly.
Top the mixture with shredded mozzarella cheese.
Bake for 15 to 20 minutes until the cheese is melted, bubbly, and beginning to brown.