Season pork with salt. Heat oil in an ovenproof skillet or small Dutch oven over medium-high heat. Place tenderloin in skillet and brown on all sides. Add onion and cook 3 minutes more, stirring onion and turning meat frequently.
Stir in 1/4 cup of the rum, broth, water, and TABASCO® SWEET & Spicy Sauce and bring to a boil. Cover skillet and transfer to a 350° oven; bake for 25 minutes.
Remove pork to a cutting board. Place skillet over high heat and bring sauce to a boil; cook until thick, about 7 minutes. Add the remaining 1 tablespoon rum and cook 1 minute longer. Slice pork and serve with sauce.
Makes 4 servings.