Meanwhile, heat 2 tablespoons oil in small saucepan over medium-high heat until almost smoking, and cook onions until soft, about 4 to 5 minutes. Add garlic and gingerroot, and cook an additional 2 minutes.
Add rum and reduce until completely dry.
Add 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 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 molasses glaze. Continue grilling for 3 minutes. Turn over, baste and continue grilling until filets reach 135°F on an internal meat thermometer for medium-rare doneness.
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