Whisk the brown sugar, honey, butter in a small saucepan over low heat until butter is melted and smooth. Off heat, stir in the mustard, soy sauce, olive oil, and ginger.
Heat the grill to medium-heat. Coat the salmon in the vegetable oil and season with salt and pepper. Place the salmon on the grill and baste with the brown sugar mixture. Grill 6 to 8 minutes, flipping once and continuing to baste.