1. Melt butter in a 2-quart saucepan over medium-high heat; add shallots and cook 4 minutes, until they begin to brown. Add bourbon, ketchup, vinegar, maple syrup, molasses, Worcestershire sauce, 1/2 teaspoon salt and 1/2 teaspoon pepper; bring to boil, reduce heat and simmer 20 minutes. (Can be made ahead. Cover and refrigerate up to 2 days.)
2. Heat grill.
3. For the rub, combine paprika, sugar, chili powder, 1 teaspoon salt and 1/2 teaspoon freshly ground pepper. Coat beef with rub.
4. Remove 2/3 cup Bourbon Sauce for basting. Cover and grill beef 30 minutes, turning two or three times. Baste with sauce. Cover and grill 30 to 35 minutes more, turning occasionally, until an instant-read meat thermometer registers 135 degrees F. Transfer to cutting board and let stand 10 to 15 minutes. (Internal temperature will increase to 140 degrees F to 145 degrees F for medium-rare.)
5. Reheat remaining bourbon sauce in saucepan. Slice beef and arrange on platter. Transfer sauce to serving bowl and serve with beef.