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.