Mince together garlic, shallots and ginger in a food processor. Add rum, lime juice, black pepper, chili powder and kosher salt and blend until smooth. Rub onto tenderloins and refrigerate overnight or no less than six hours.
Dechill meat for tenty minutes. Heat olive oil in medium-heat skillet and sear tenderloins on both sides, about five minutes. Reduce to low heat and ook coered for an additional 12-15 minutes or until oooked to 135-140F.