Adjust rack to upper position and preheat oven to 425 degrees. Wash and dry all produce. Halve, peel, and thinly slice onion. Mince garlic. Peel and cut carrots diagonally into 1-inch-thick pieces. Trim and thinly slice mushrooms. Peel and dice potatoes into 1/2-inch pieces. (TIP: For speedier spud prep, skip the peeling.)

Toss carrots on a baking sheet with a large drizzle of oil, salt, and pepper. Roast, flipping halfway through, until browned and tender, about 25 minutes. Meanwhile, place potatoes in a medium pot with enough salted water to cover by 2 inches. Boil until tender, about 15 minutes, then thoroughly drain.

Meanwhile, heat a large drizzle of oil in a medium pan over medium-high heat (use a nonstick pan if you have one). Add onion and cook, stirring occasionally, until browned and softened, about 15 minutes. Add a splash of water every now and then, scraping up any browned bits on bottom. Season with salt and pepper. Transfer to a small bowl.

Return drained potatoes to empty pot. Stir in sour cream, salt, and pepper. Mash over low heat until smooth. Keep covered until ready to serve. Pat steak dry with paper towels; season with salt and pepper. Wipe out pan used for onion, then heat a large drizzle of oil in it over medium-high heat. Add steak and cook to desired doneness, 3-6 minutes per side. Remove from pan and set aside to rest.

Add 2 TBSP butter and mushrooms to same pan over medium-high heat. Cook, stirring, until softened, 2-4 minutes. Add garlic and cook until fragrant, about 1 minute. Stir in demi-glace and 1/4 cup water. Bring to a boil, then lower heat to a simmer. Stir in mustard. Simmer until slightly thickened, 1-2 minutes. Season with salt and pepper.

Slice steak against the grain. Divide potatoes, carrots, and steak between plates. Top potatoes with onion. Top steak with sauce, making sure to include mushrooms.