Sprinkle beef evenly with ½ teaspoon salt and ¼ teaspoon pepper. Brown fillets in hot oil in an ovenproof or cast-iron skillet over medium-high heat 3 minutes on each side. Remove fillets, reserving drippings in skillet.

Melt butter in drippings over medium-high heat. Add yellow and red onion rings, and sauté 5 minutes.

Add green onions, shallots, and garlic, and sauté 10 to 15 minutes or until lightly browned.  Stir in cognac and broth; cook over medium-high heat, stirring constantly, until liquid evaporates (about 5 minutes). Place fillets on top of onion mixture in skillet. Cover with aluminum foil.

Bake at 400° for 15 to 20 minutes or until a meat thermometer inserted into thickest portion of meat registers 135° (medium rare).

Remove fillets from skillet, reserving onion mixture in skillet; cover fillets loosely, and let stand at room temperature 10 minutes.

Cook onion mixture over medium heat, stirring constantly, 5 minutes or until liquid evaporates.
Add salt and pepper to taste. Serve with fillets.