Branzino is an innocuous enough fish; it is firm-fleshed but delicate so you need to give it additional flavors with which to work. It is most often served and sold as whole fish but I was not in the mood for the work involved in eating that.
My fishmonger took the fillets off the bone and sent me home with the heads and bones for stock (which immediately went into the freezer for a later date). The fillets were not skinned but, rather than amping that up and crisping the skin up prior to eating the fish, I decided that the branzino was too delicate for that and cooked them as is. Once cooked, the skin peels right off.
I don't know why I decided to mix Angustura bitters with butter besides the fact that I had what the French refer to as "un fond de bouteiile" to dispose of and thought that the floral notes of the bitters would work with fish. The problem is that I liked this quick sauce so much that bitters are now on my grocery list so that I can make this again.
8 branzini fillets (not a typo it takes multiple fish to get 8 fillets)
3 Tbsps unsalted butter
2 tsps Angustura bitters
Salt to taste
Preheat oven to 375.
While the oven is preheating, melt the butter in an oven safe skillet on the stove top. You may need 2 pans for this in which case, divide the butter evenly between the 2 pans.
Remove the pan from the heat and add the bitters. Mix together. Again, if using 2 pans, divide the bitters equally between the 2 pans.
Salt the fish and place the fillets skin side up in the bitters butter in the pan(s). You want the flesh to cook in the butter.
As soon as the temperature reaches 375, place the pan(s) in the oven and bake for 10 minutes.
Remove from the oven. Using the tines of a fork, carefully lift off one edge of the skin, the rest should come off easily, in one piece.
Place 2 fillets on each plate, salt lightly and drizzle with the remaining bitters butter.