Get a premium steakhouse experience right at home! You'll cook up some ultra-tender filet mignon and a rich Bordelaise sauce of red wine, butter, and minced shallots. The dish is made even more luxurious (and comforting) with duchess potatoes, which you'll whip and then bake to fluffy perfection. Pour yourself a glass of wine and indulge!
Peel potato and cut into 1" cubes. Bring a small pot with potato cubes, 1 tsp. salt, and enough water to cover to a boil. Reduce to a simmer and cook until tender, 15-18 minutes. While potatoes simmer, mince chives. Trim bottom ends from broccolini. Peel and mince shallot. Pat steaks dry.
Make the Duchess Potatoes
Drain potato in a colander and return to pot. Add sour cream, liquid egg, half the butter, and chives to pot and mash until smooth. Season with ¼ tsp. salt and a pinch of pepper. Transfer to a small casserole dish or two oven-safe ramekins and place on foil-only prepared baking sheet. Use fork tines to pull potatoes into small peaks, forming decorative ridges. Bake until potato ridges turn golden brown, 15-22 minutes. While potatoes cook, sear steaks.
Sear the Steaks
Place a medium non-stick pan over high heat. Season steaks on both sides with ¼ tsp. salt and a pinch of pepper. Add 1 tsp. olive oil and steaks to hot pan and cook until browned, 2-3 minutes per side. Transfer steaks to one side of sprayed prepared baking sheet and set aside. Reserve pan; no need to wipe clean.
Roast the Steaks and Broccolini
Place broccolini on same baking sheet as steaks and toss with 1 tsp. olive oil and a pinch of salt and pepper. Roast until steaks reach a minimum internal temperature of 145 degrees, 8-14 minutes. Tent steaks and broccolini with foil and rest steaks at least 5 minutes.
Make the Sauce
Return pan used to sear steaks to medium-high heat. Add 1 tsp. olive oil and 2 Tbsp. shallot to pan and cook 30 seconds. Add red wine and reduce to a syrupy consistency. Add demi-glace and ¼ cup water and cook until slightly thickened, 1 minute. Remove from burner and swirl in remaining butter. Strain sauce if desired.
Finish the Dish
Arrange roasted broccolini and steak on a plate. Spoon sauce onto plate and serve duchess potatoes on the side. Garnish potatoes with remaining chives.