Wash and dry all produce. Adjust rack to upper position and preheat oven to 425 degrees. Halve, peel, and thinly slice onion. Thinly slice or mince garlic. Halve carrots lengthwise through stems. Trim, then thinly slice mushrooms. Peel potatoes, then cut into 1/2-inch cubes. Pick parsley leaves from stems; discard stems. Finely chop leaves.

Toss carrots with a large drizzle of oil on a baking sheet. Season with salt and pepper. Roast in oven under tender and slightly charred at edges, 20-25 minutes. Meanwhile, place potatoes in a medium pot with enough salted water to cover by 1 inch. Bring to a boil. Cook until tender, about 15 minutes, then thoroughly drain.

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 very soft, about 15 minutes. Add a splash of water every now and then, scraping up any browned bits on bottom. Transfer to a small bowl. Season with salt and pepper.

Return drained potatoes to empty pot. Place over low heat. Mash with a potato masher until smooth. Stir in sour cream. Season with salt and pepper. Keep over low heat. Wipe out pan used for onion, then heat a large drizzle of oil in it over medium-high heat. Pat steak dry with a paper towel and season with salt and pepper. Add to pan and cook to desired doneness, 3-6 minutes per side.

Remove steak from pan and set aside to rest. Add 2 TBSP butter and mushrooms to same pan over mediumhigh heat. Cook, tossing, until softened, 2-4 minutes. Toss in garlic and cook until fragrant, about 1 minute. Stir in demiglace and 1/4 cup water, then bring to a boil. Lower heat and reduce to a simmer. Stir in mustard. Let simmer until slightly thickened, 1-2 minutes. Remove pan from heat and stir in half the parsley.

Season sauce with salt and pepper. Divide potatoes and carrots between plates. Spoon onion over potatoes. Slice steak against the grain, then arrange on top of potatoes and onion. Spoon sauce over steak, making sure to include mushrooms. Garnish with remaining parsley.