Preheat broiler. Place an oven rack in the second position from the top if you have five rack positions in your oven, about 5 inches from the broiler. Preheat the broiler. Broilers generally preheat to about 500 degrees Fahrenheit.
Prepare baking sheet. Line a baking sheet with aluminum foil and lightly brush with oil where you will place the salmon.
Make glaze mixture. Whisk together the mustard, melted butter, brown sugar, honey, paprika, chili powder, salt, pepper, and lemon zest in a small bowl.
Brush mixture over salmon. Place salmon portions on the prepared baking sheet. Brush the mixture evenly over each salmon portion. If you use three salmon portions, you may have a little leftover glaze.
Broil. Place the baking sheet in the oven on the oven rack in the second position and broil the salmon for 8-11 minutes based on the thickness of the salmon and the desired doneness.
Rest and garnish. Carefully remove from the oven, and let fish rest for 5 minutes. The fish will continue to cook slightly. Remove the skin before serving if desired. Garnish with chopped parsley and serve immediately.