Preheat oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
Bring a large pot of salted water to a boil. Add broccoli and cook for 2 minutes. Drain and set aside.
In a large skillet over medium-high heat, cook chicken pieces until golden and cooked through (about 5-7 minutes). Remove and set aside.
In the same skillet, melt 2 tbsp butter over medium heat. Add onion and cook until softened, about 3 minutes. Add garlic and cook for 1 minute.
Sprinkle flour over the onion mixture and stir constantly for 1 minute. Gradually whisk in chicken broth and heavy cream. Bring to a simmer and cook until thickened, about 2-3 minutes.
Remove from heat. Stir in sour cream, salt, pepper, paprika, and 1 cup of cheddar cheese until melted and smooth.
Add the cooked chicken and broccoli to the sauce and stir to combine. Transfer to the prepared baking dish.
In a small bowl, mix breadcrumbs with 2 tbsp melted butter. Sprinkle over the casserole along with the remaining 1/2 cup cheddar cheese.
Bake for 20-25 minutes, until bubbly and golden on top. Let rest for 5 minutes before serving.
Tips
For a lighter version, use half-and-half instead of heavy cream.
To make ahead, assemble casserole without breadcrumb topping, cover, and refrigerate up to 24 hours. Add topping and bake, adding 10 minutes to cooking time.
Leftovers can be stored in an airtight container in the refrigerator for up to 3 days.