In a small bowl, mix soy sauce, brown sugar, water, garlic, ginger, and black pepper to make the marinade.
Place salmon fillets in a shallow dish and pour the marinade over them. Cover and refrigerate for at least 30 minutes.
In a large skillet, heat vegetable oil over medium-high heat.
Remove salmon from marinade and place in the skillet, skin side down. Reserve the marinade.
Cook salmon for about 4-5 minutes on each side or until cooked to your desired level of doneness.
While salmon is cooking, pour the reserved marinade into a small saucepan and bring to a simmer. Cook for 5 minutes to thicken.
Serve salmon with the thickened marinade drizzled on top.