Directions: Sprinkle tenderloin with 1/2 teaspoon salt and 1/2 teaspoon pepper.
Secure with string at 1-inch intervals. Brown tenderloin on all sides in hot oil in a heavy roasting pan or ovenproof Dutch oven. Remove tenderloin, reserving drippings in pan. Add butter to drippings and cook over medium-high heat until melted. Add purple onion rings, and saute 5 minutes. Add green onions, shallot, and garlic; and saute 10 minutes.
Stir in cognac and broth; cook over high heat, stirring constantly, until liquid evaporates (about 5 minutes). Place tenderloin on top.
Bake, covered, at 400F degrees for 45 minutes or until a meat thermometer inserted into thickest portion of tenderloin registers 145 degrees (medium rare).
Remove tenderloin from roasting pan, reserving onion mixture in pan; cover tenderloin loosely, and let stand at room temperature 10 minutes.
Cook onion mixture over medium heat, stirring constantly, 3 to 5 minutes or until liquid evaporates. Stir in remaining 1 teaspoon salt and remaining 1/2 teaspoon pepper. Serve with sliced tenderloin.
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