Rinse your eelpout steaks or filets in cool, running water to remove any scales or stray bits of skin. Pat them dry with paper towels.

Season both sides of the fish with plain table salt and finely ground pepper. Alternatively, use coarse salt and cracked pepper, which add texture in addition to flavor.

Trim your eelpout so that each piece of fish is no thicker than about 1 to 1 1/2 inches, to ensure that the outside does not char or dry out before the inside has cooked through.

Coat whatever cooking surface you have chosen to use with either a thin layer of olive oil, vegetable oil or canola oil or a light coating of nonstick cooking spray.

Heat your grill or frying pan to medium-high. Preheat a broiler on high and your oven to 425 degrees Fahrenheit.

Brush the top of your eelpout with a bit of melted butter. Add a squeeze of lemon juice and season the fish, using Herbes de Provence, lemon pepper and basil, as desired. Use a light hand, because eelpout has a delicate flavor.

Cook the eelpout for 5 minutes per every inch of thickness no matter which method you use. Turn the fish carefully with tongs. Brush with butter and season the other side. Cook it for another 5 minutes per every inch of thickness. Check the fish for doneness by inserting an instant-read thermometer into the thickest part. The fish is done when it reaches an internal temperature of 145 F, and the flesh flakes easily.

Fill a pot two-thirds full with water, or use the regional trick of cooking the fish in clear citrus-flavored soda. Bring the liquid to a rolling boil over high heat.

Add chunks of eelpout and stir them into the boiling liquid. Bring the liquid back to a rolling boil and cook the eelpout for 5 minutes.

Drain the eelpout and serve it with melted butter for dipping, just as you would serve lobster meat.