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Step 1
Preheat oven to 425 degrees F.
Step 2
In a saucepan, over medium heat, simmer 4 cups of chicken stock until reduced by half.
Step 3
In a large saute pan, heat 1 tablespoon of the olive oil over high heat until hot but not smoking.
Step 4
Season the filets mignons with salt and pepper and add to the hot pan. Sear on both sides until browned nicely, about 2 to 3 minutes on each side, and transfer to oven for about 3 to 4 minutes for rare, 5 to 6 minutes for medium. Remove from oven and let rest.
Step 5
Drain excess oil from the pan and return to medium heat; add the shallots and saute briefly; add the red wine and thyme and simmer for 1 minute. Add the chicken stock and continue simmering to reduce to 1 cup; remove from heat and swirl in butter. Season with salt and pepper, to taste.
Step 6
In another large saute pan over high heat, heat the remaining olive oil until hot but not smoking. Season the shrimp with salt and pepper. Saute the shrimp for about 2 minutes on each side and remove from the pan to a plate.
Step 7
Drain any excess oil from the pan and return to the stove. Deglaze with the white wine and reduce by 1/Slowly add butter, stirring to emulsify; finish with the chives. Season with salt and pepper, to taste.
Step 8
To serve. On each plate arrange 1 filet and 2 shrimp, spoon about 1 tablespoon of the red wine sauce on the filet and spoon about 1 tablespoon of the white wine sauce over the shrimp. Serve warm.