Preheat the oven to 350°F (175°C) and spray a 9x13-inch baking dish with cooking spray or lightly coat with olive oil.
In a large mixing bowl, combine the heavy cream, salt, pepper, thyme, and paprika. Stir until well blended.
In the baking dish, layer the chicken breasts evenly. Pour half of the cream mixture over the chicken.
Add the broccoli and cauliflower florets, spreading them evenly over the chicken.
Sprinkle the diced onion and minced garlic over the vegetables.
Pour the remaining cream mixture over the top and add the shredded swiss cheese evenly across the entire casserole.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
After 30 minutes, remove the foil and bake for an additional 15 minutes, or until the chicken is cooked through and the cheese is bubbly and golden.
Let the casserole cool for 5-10 minutes before serving.