2 1/2 Tbsp unsalted butter cold and cut into pieces
1/2 cup fresh tangerine juice
1 Tbsp shallot finely chopped
1/4 tsp kosher salt
cayenne pepper to taste
1/2 tsp fresh lemon juice
1 tsp fresh cilantro finely chopped
1 Tbsp heavy cream to stablize
Preheat a large non-stick skillet over medium-low heat for 5 minutes.
Lay the fillets on a piece of wax paper and blot dry with paper towels. Season the fillets with salt and pepper. Put the flour on a plate. Dredge the rounded-sides of the fillets in the flour and shake off any excess.
Raise the heat to medium-high and add 2 tablespoons of butter to the hot skillet. When the butter stops foaming, add the fillets to the pan, rounded-side down, and cook, lightly shaking the skillet occasionally, until golden brown, about 2 minutes. Turn off the heat, flip the fillets with a spatula, and let the fillets finish cooking in the residual heat in the pans, about 2 minutes more. Transfer the fillets to 4 warm plates and cover loosely with foil.
Boil tangerine juice with shallot in a 2-quart heavy saucepan over moderate heat until reduced to about 2 tablespoons, 4 to 5 minutes. Reduce heat to moderately low, then whisk in 1 tablespoon butter, whisking constantly. Add remaining butter, 1 tablespoon at a time, whisking constantly, adding each piece before previous one has completely melted, and lifting pan from heat occasionally to cool mixture. Remove from heat and stir in salt, cayenne, and lemon juice. Gradually whisk into beurre blanc and finish by folding in chopped cilantro.
Remove foil from the plates of fish and spoon sauce over the finished fillets.