In a bowl, mix together the brown sugar, salt, crushed red pepper flakes, mint leaves, and brandy to make a paste. Rub the paste all over the salmon, wrap in plastic wrap, and refrigerate 4 hours to overnight.
Preheat an outdoor grill for high heat, and lightly oil the grate. Place soaked alder chips in a small disposable aluminum pie pan or piece of aluminum foil at the back of the grill, under the grate. Allow the wood chips to begin smoking, then turn the heat to the lowest setting, position the salmon on the grate, and close the lid. Cook and smoke the salmon until it has turned a red-brown color and flakes easily, about 45 minutes.
