Pat the catfish dry, season with salt and pepper, and dredge lightly in flour.
Heat olive oil and 1 tbsp butter in a large skillet over medium-high heat.
Cook the catfish undisturbed for 3 to 4 minutes until golden, flip, and cook 2 to 3 minutes more until it flakes easily. Remove to a plate.
Lower heat to medium, add remaining butter, garlic, and Calabrian chilies with their oil. Stir 30 seconds until fragrant.
Add radicchio wedges cut side down and cook 2 to 3 minutes per side until charred and softened.
Squeeze lemon juice over the radicchio and toss.
Plate the radicchio, top with catfish, garnish with parsley, and serve with lemon wedges.