Set the grill for indirect heat, preheating to very hot (500 degrees), then turn it down to 300 degrees, or as low as you can go.

Prepare one large foil tray for cooking the salmon. [Make your own: Layer two 16-inch pieces of foil (one directly on top of the other) and fold up each side about an inch, to create a rectangular “tray.”

Wash and pat-dry the salmon (with paper towel). Place on the foil tray.

In a small bowl mix together the butter, shallots, lime, dill, brown sugar, and pepper. Press evenly over the salmon. Heavily salt the salmon filet.

Place the salmon tray on the grill. Grill the salmon at 300 degrees, or as low as you can go. Slow-grilling salmon is what makes it good.

Cover the grill and cook until the salmon just begins to flake easily, and is almost completely opaque throughout, 7 to 8 minutes, or until done to your liking. Use a meat thermometer, with the thickest part of the salmon cooked at 130 degrees, or using the back of a spatula, until firm (and not spongy).

Transfer the salmon to individual plates; serve immediately.