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.
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.
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.
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).
Adapted from The Lee Bros. Simple Fresh Southern cookbook.