Cook the wild rice according to package instructions (about 45–55 minutes). This can be done in advance.
In a large bowl, mix together cream of chicken soup, sour cream, and chicken broth. Season with pepper and adjust salt if needed.
Add shredded chicken and cooked wild rice. Stir until everything is well coated and creamy.
Transfer the mixture to a lightly greased 9x13 baking dish. Spread evenly and top with shredded cheddar cheese.
Preheat oven to 350°F (175°C). Bake uncovered for 35–40 minutes until bubbly and golden on top.
Let rest for 5 minutes before serving.