Melt butter in a large pan. Add garlic and cook for 2-3 minutes.
Place fennel wedges in pan and cook for 3-4 minutes without stirring. Flip fennel over and cook on other side.
Pour vegetable broth into pan, bring to a simmer, and cover for 10-12 minutes.
Meanwhile, combine milk and egg in a wide bowl.
In a separate bowl, combine cornmeal, flour, salt, pepper, and cayenne pepper. Dry off fish fillets and dip first into milk and egg bowl, then into cornmeal bowl, making sure that both sides are well coated.
Heat oil for the fish in a large pan. Once oil is hot, place fish in pan and fry for 4-5 minutes on each side, depending on thickness of fish.
Transfer fish to a plate with paper towel to soak up some of the oil.
To finish off the fennel, add salt and pepper and a squeeze of lemon juice.
Recipe by Things I Made Today at https://www.thingsimadetoday.com/2013/05/05/cornmeal-crusted-catfish-and-braised-fennel/