Combine the flour, peppers, and salt. Dredge the fish fillets in the flour mixture and shake off any excess.
Melt 2 tablespoons of the butter in a heavy saucepan and heat until the butter is nut brown and foaming. Be careful not to burn. Place the fish fillets in the pan, skin side down, and sauté until cooked on that side, about 3–4 minutes. Carefully flip the fillets over and sauté on the other side for another three minutes or so.
Drain off the excess butter and reduce the heat to a simmer. Add the capers, caper berries, lemon juice, and wine. Cook for about 5 minutes, then enrich the sauce with the remaining 4 tablespoons butter.
Remove the fish to a serving platter, pour the sauce over the fish, and garnish with the chopped parsley and lemon slices. Accompany with rice and asparagus if desired.