Whisk together the soy sauce, olive oil, brown sugar, lemon pepper, and garlic in a shallow dish; lay the salmon fillets into the mixture with the skin side facing up. Allow to marinate in the refrigerator 4 to 8 hours or overnight.
Preheat the oven's broiler and set the oven rack about 6 inches from the heat source. Remove salmon from the marinade and arrange on a baking sheet. Discard the marinade.
Cook the salmon under the broiler until lightly browned and the flesh flakes easily with a fork, 7 to 10 minutes. Allow the salmon to rest 5 minutes before slicing and serving.