Adjust rack to top position and preheat oven to 425 degrees. Wash and dry all produce. Trim, peel, and slice carrots into 1-inch pieces on a diagonal. Dice potatoes into 1/2-inch pieces. Halve, peel, and mince shallot. Quarter lemon. Reserve 1 whole sprig thyme, then pick remaining thyme leaves from stems and roughly chop until you have 1 tsp (2 tsp for 4 servings).

Toss carrots on a baking sheet with a large drizzle of oil. Season with salt and pepper. Roast, tossing halfway through, until browned and tender, 2530 minutes (after 10 minutes, we’ll start the steak).

Meanwhile, place potatoes, whole garlic cloves, and reserved thyme sprig in a medium pot with enough salted water to cover by 2 inches. Boil until tender, about 15 minutes. Reserve 1/4 cup cooking water (1/2 cup for 4 servings), then drain. Remove and discard thyme. Return potatoes and garlic to pot and mash with 2 packets sour cream (4 packets for 4), 1 TBSP butter (2 TBSP for 4), salt, and pepper. Add reserved cooking water, a splash at a time, until smooth. Cover to keep warm.

Once carrots have roasted 10 minutes, pat steak dry with paper towels, then season all over with salt and pepper. Heat a drizzle of oil in a large pan over medium-high heat. Add steak and cook until browned and cooked to desired doneness, 3-6 minutes per side. Transfer to a cutting board to rest at least 5 minutes. Wipe out pan.

Heat a drizzle of oil in pan used for steak over medium-high heat. Add shallot and chopped thyme. Cook, stirring, until softened, about 1 minute. Add demi-glace and 1/4 cup water (1/3 cup for 4 servings). Cook, stirring, until thickened, about 2 minutes. Remove from heat and stir in remaining sour cream and a squeeze of lemon juice (to taste).

Toss roasted carrots with honey, a squeeze of lemon juice, and chili flakes (to taste). Thinly slice steak against the grain. Divide carrots, mashed potatoes, and sliced steak between plates. Top steak with sauce. Serve with remaining lemon wedges on the side.