Preheat the oven broiler to high and move the oven rack to the top position so the fish will be close to the heat source.
In a mixing bowl, combine the brown sugar, smoked paprika, garlic powder, salt, black pepper, and crushed red pepper flakes until evenly mixed.
Place the salmon fillet skin-side down on a baking sheet. Pat the top dry with a paper towel if needed.
Rub the brown sugar spice mixture evenly over the top of the salmon, covering the entire surface.
Broil the salmon for 5–6 minutes with the top of the fillet toward the broiler, until the sugar begins to caramelize and turns golden. Watch closely to avoid burning.
If your salmon is thicker than 1 inch and needs more cooking, either flip the fillet (remove skin first) and broil an additional 2–3 minutes, or move the oven rack down one level and continue broiling until cooked through without burning the sugar.
Remove from the oven and serve immediately.