With a sharp knife, cut strips of lemon zest 1/2 inch wide and 1 inch long. Set aside. (Take care to cut only the zest and none of the pith.)

Melt the butter in a heavy saucepan over high heat. When it begins to bubble, remove from the heat and skim off the foam. Strain the clear liquid at the top and discard any milky residue.

Heat half the clarified butter in a large skillet and sauté the monkfish, turning occasionally, until nearly done, about 10 minutes. Add the lemon zest and sauté until fish is browned, about 3 to 5 minutes.

Heat the remaining clarified butter in a small skillet until brown, about 7 minutes. Add the capers and sauté until crispy, 2 to 3 minutes.

Serve the monkfish fillets with the sautéed lemon zest, browned butter, and capers.