1. Stir together first 4 ingredients and 2 tsp. salt in a 2-qt. measuring cup until salt dissolves. Reserve 1 1/4 cups. Pour remaining mixture into a zip-top plastic freezer bag. Add tenderloins; press out air, seal, and chill 2 to 4 hours, turning every 30 minutes.
2. Preheat oven to 450°. Remove tenderloins from marinade, discarding marinade. Pat tenderloins dry. Brush with 1 Tbsp. oil, and sprinkle with pepper and remaining 1 tsp. salt.
3. Cook tenderloins, in batches, in remaining 1 Tbsp. hot oil in a large cast-iron skillet over high heat 2 to 3 minutes on each side or until browned. Transfer to a plate; discard oil. Reduce heat to medium. Add butter and shallots to skillet, and cook, stirring constantly, until butter melts. Stir in flour. Cook, stirring often, 3 minutes or until shallots are tender. Whisk in reserved 1 1/4 cups sherry mixture, and bring to a simmer. Simmer 2 to 3 minutes or until slightly thickened. Remove from heat, and season with salt and pepper to taste. Place tenderloins in a 13- x 9-inch baking dish; pour sauce over tenderloins.
4. Bake at 450° for 10 to 12 minutes or until a meat thermometer inserted into thickest portion registers 165°. Transfer tenderloins to a cutting board, reserving gravy in baking dish. Cover loosely with foil, and let stand 10 minutes. Cut into 1/2-inch-thick medallions, and serve with gravy.
Brought to the table by cookbook authors Matt Lee and Ted Lee (adapted from The Lee Bros. Simple Fresh Southern cookbook).