In a large shallow dish, combine the first 9 ingredients. Add catfish, 1 fillet at a time, and turn to coat.
Place a large cast-iron skillet on a grill rack over medium-high heat. Melt butter in the skillet; add catfish in batches, if necessary. Grill, covered, until fish just begins to flake easily with a fork, 5-10 minutes on each side. If desired, serve with lemon wedges and fresh parsley.