Meanwhile, heat 2 tablespoons oil in a small saucepan over medium-high heat until almost smoking, and cook the onions until soft, about 4 to 5 minutes. Add the garlic and gingerroot, and cook an additional 2 minutes.
Add the rum, and reduce until completely dry.
Add the molasses, orange juice and pepper. Season with salt, as desired, and cook until reduced to 1 cup, about 15 to 20 minutes. Let cool at room temperature.
Brush the beef with remaining olive oil, and season with salt, as desired. Grill mignons 4 minutes until seared on one side. Turn over, and baste with the Molasses Glaze. Continue grilling for 3 minutes. Turn over, baste, and continue grilling until the filets mignons reach 135°F on an internal meat thermometer for medium-rare doneness.