I would recommend a doctor, but he might not be a good eeler.

What excuse do you have for being a git on GS? Oh yes you are the resident moron and annoyance aren't you eely?
So what will be your next handle? You will probably need to come up with one soon.
I fart in your general direction! Your mother was a hamster and your father smelt of elderberries!
Yes, the onions will soften faster than the celery, which will soften faster than the carrots, but that is fine. You end up with a broad variety of textures in this dish, and a nice deep flavor. Braising them in red wine has the advantage of masking the muddy flavors that may come out if the eel hasn't been properly purged. Using the same basic technique, you can also braise them in beer or stock.
My last good eel recipe is probably the easiest... Once you have dispatched the eel with a nail through the head and waited for it to stop writhing, wash it down with vinegar and coarse salt to remove the slime. Gut the creature and throughly scub out the inside. If you want to leave the head attached, trim out the gills with some shears. Also trim off the fins. Marinate overnight in a brine of one quart water, two quarts vinegar, one quarter cup salt, one tablespoon sugar and some allspice and juniper berries, brought to a boil and then cooled.
(The fastest way to do that, by the way, is to boil the vinegar with the seasonings, then add the water in the form of ice cubes. Make sure the brine is completely cool.)
When it is time to cook, rinse the eel well, then fill the body cavity with fresh thyme and thin slices of lemon.
Now, depending on your taste you can either coil the eel - start with the tail at the center and winding it into a sort of flemish coil, with the belly side up, then secure it with either skewers as you would a rope sausage or with butcher's twine - or grill it lying straight. I think grilling it straight works better because you can char the skin on all sides instaed of leaving a slimy layer of skin where the coils were touching.
Both make for startling presentations, so if you or your guests are squeamish, cut the eel into six- or seven-inch lengths.
Grill the eel over very high heat. Try to keep it well above the coals, if you can, because it will drip quite a bit and flair up a bit.
Let the skin char while the inside cooks through, then peel and eat with beer. Be prepared to use your fingers.