In a bowl, combine brown sugar, paprika, garlic powder, salt, pepper and red pepper flakes, mixing well.
Heat the broiler on your oven to high, and place the oven rack as high as it will go. Place salmon filet on a baking sheet and rub brown sugar mixture all over top. I tend to buy a piece of salmon with skin on, so I place the salmon skin side down on the baking sheet and just rub the spices on top. Place under the broiler and broil for 5-6 minutes, until sugar begins to caramelize and get golden. Serve immediately!
It is pretty important to use a piece of salmon that is no thicker than one inch – if your salmon is thicker, I suggest flipping the salmon after 5 minutes and broiling for another 2-3 (this requires that the skin be removed) OR lowering your oven rack one level down – this will prevent the sugar from burning since you have to broil longer. After the initial 5 minutes, the sugar may be a bit smokey but it should not burn.