How to Make It
In a small bowl, combine 1/4 cup of the cream and the mustard. Let sit about 10 minutes.
In a shallow dish, combine the egg with the 1 tablespoon cream. In another shallow dish, combine the cornmeal with 1 teaspoon of the salt and the pepper. Dip the fillets into the egg mixture and then into the seasoned cornmeal. Shake off the excess cornmeal.
In a large nonstick frying pan, heat 2 tablespoons of the oil over moderate heat. Add half the cornmeal-coated fish and fry, turning once, until the fillets are golden on the outside and just done in the center, about 4 minutes per side for 3/4-inch-thick fillets. Drain the fish on paper towels. Repeat with the remaining 1 tablespoon oil and fish fillets. Wipe out the pan.
Put the pan over moderate heat. Add the broth and garlic and bring to a simmer. Stir in the remaining 1/2 cup cream; simmer until reduced to approximately 1/3 cup, about 2 minutes. Stir in the reserved mustard cream and the remaining 1/4 teaspoon salt and simmer until warm through, about 1 minute longer. Serve the catfish fillets topped with the sauce.