Steps:
- For the beef tenderloin: Preheat a saute pan or cast-iron skillet over high heat. Lightly oil the steaks. Place the steaks in the very hot pan and get a good sear on both sides. Cook for 6 to 7 minutes per side for medium-rare. Remove the steak from the pan and let rest in a warm spot for 7 to 8 minutes.
- For the mushroom sauce: Drain the fat from the pan. Add the shallots, bring the pan to a medium heat and season with salt. Cook the shallots for 3 to 4 minutes, and then add in the garlic. Cook the garlic and shallots together for 2 to 3 minutes.
- Add the mushrooms, season with salt and stir to coat with the oil. Cook the mushrooms until they look soft and wilted, 4 to 5 minutes.
- Add the veal demi-glace. Bring to a boil and reduce to a simmer and simmer for 4 to 5 minutes; the consistency should be almost as thick as gravy. If it is still thin, let it simmer for another couple of minutes until it does thicken.
- Check the consistency by coating a spoon with the sauce, turn the spoon over and draw a line down the middle of the spoon with your finger. If your finger leaves a track down the spoon without moving, then it is ready! Taste and adjust the salt, if needed.
- For the twice-baked potato mash and green beans: Add the potatoes to a pot of salted water. Turn the heat to medium and cook until the potatoes are fork tender, 20 to 25 minutes. Drain the potatoes well and pass through a food mill or ricer. Stir in the sour cream and heavy cream. Fold in the broccoli and Cheddar. Taste and season with salt as needed.
- Bring a pot of salted water to a boil. Add the green beans and cook until just tender, about 2 minutes. Remove from the water and immediately add to a salted ice bath. Heat the olive oil in a medium saute pan. Add green beans and saute quickly until heated through.
- Serve the filets with the mushroom sauce on top and the twice-baked potato mash and green beans on the side.
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