Thaw filets in refrigerator overnight, then bring to room temperature for 20 to 25 minutes and pat dry with paper towel.
Liberally season filets with salt and pepper on all sides.
Add grapeseed oil to a heavy medium-sized cast-iron pan and bring to medium-high heat.
Add filets to pan and sear for 3 minutes on one side.
Add 1 tablespoon butter and duck fat to pan, flip filets, then butter-baste for about 30 seconds.
Allow filets to finish cooking in pan for another 3 to 4 minutes for medium-rare (130 to 140 degrees Fahrenheit) doneness. Refer to Omaha Steaks cooking chart for different preferred doneness.
Remove filets from pan and allow to rest 6 to 7 minutes.
Discard half of pan drippings and add olive oil; reduce heat to medium.
Add shallots to pan and sauté for about 45 seconds, then add garlic and sauté for another 10 seconds.
Add balsamic vinegar, beef stock, and sweet vermouth to pan and bring to a boil.
Reduce heat to low and simmer pan sauce for about 2 minutes until reduced in volume by half and slightly thickened.
Remove pan from heat and stir in remaining 1 tablespoon of cold unsalted butter until sauce emulsifies; season to taste with salt and pepper and serve sauce over filets.