Preheat your oven to 350°F (175°C).
In a large skillet, heat the olive oil over medium heat. Add the diced onion and minced garlic, sautéing until the onion is translucent, about 3-4 minutes.
Add the broccoli florets to the skillet and cook for another 3-5 minutes, until tender.
In a large mixing bowl, combine the cooked chicken, heavy cream, cream cheese, and dried thyme. Stir well until the mixture is smooth and creamy.
Add the sautéed mixture from the skillet into the bowl and season with paprika, salt, and pepper. Mix everything until well combined.
Pour the chicken and broccoli mixture into a greased 9x13 inch baking dish. Spread it evenly.
Top with shredded cheddar cheese, spreading it evenly over the casserole.
Bake in the preheated oven for 25-30 minutes or until the cheese is melted and bubbly.
Remove from the oven and let it cool for a few minutes before serving.