Melt the butter in a frying pan, add the minced shallots, and cook for a couple of minutes to soften. Remove the shallots from the pan with a slotted spoon.
Cut the eels into 2-inch slices and flatten slightly. Add to the pan and fry in the butter for a minute or two just to stiffen. Lay the pieces of eel in a pie dish, and add the shallots, mushrooms, parsley, fennel, lemon zest, and n