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Heat butter and oil in a sauté pan over medium-high heat until butter melts. Add filets; sauté until an instant-read thermometer registers 130° for medium-rare, 2 minutes per side; transfer to a plate and tent with foil.
Add mushrooms to pan; sauté until browned, 3-4 minutes. Add garlic, basil, and oregano; cook 1 minute.
Coimbine cream and vermouth and stir into pan; reduce by half, 2-3 minutes. Add filets (and accumulated juices) to pan to heat through; serve filets with sauce and garnish with parsley.
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