Get your vegetables ready, peel the shallots and chop very finely, the finer the better. Chop the washed chives finely and keep a couple strands for garnish.
On moderate heat, place a frying pan and melt the butter. Once the butter is melted, place the fish pieces, and cook in the butter until lightly golden brown. Add a touch of salt. Check underneath and if light brown, flip over the fish (be gentle not to break them). Continue cooking until the butter is nutty brown. Remove the fish carefully using an egg flipper or a fish spatula and place on heated serving plates.
Deglaze pan with white wine, add the lemon zest, add the chopped shallots into the sauce. Add the cream. Season the sauce with salt and pepper.
Continue to reduce the sauce on high heat until it thickens to your liking. Add the chopped chives, mix well and pour over fish. Garnish with a couple strands of chives.