Preheat oven to 375°F (190°C). Grease a 9×9-inch baking dish with olive oil or butter.
Prepare the sauce: In a large mixing bowl, combine cream cheese, heavy cream, and chicken broth. Whisk until smooth.
Stir in garlic powder, onion powder, th
yme (if using), salt, and pepper.
Fold in shredded chicken, steamed broccoli, Parmesan cheese, and 1 cup of the cheddar cheese. Mix until evenly coated. Add a splash more broth if the mixture feels too thick.
Transfer the mixture to the prepared baking dish and spread evenly.
Top with the remaining ½ cup of cheddar cheese (add extra if desired).
Bake uncovered for 25–30 minutes, until bubbly and lightly golden on top.
