Adjust rack to top position and preheat oven to 425 degrees. Wash and dry all produce. Dice potatoes into 1/2-inch pieces. Peel and cut carrots diagonally into 1/2-inch-thick pieces. Thinly slice chives. Place potatoes in a large pot with enough salted water to cover by 2 inches. Boil until tender, about 15 minutes. Drain and return to pot.

While potatoes cook, toss carrots on a baking sheet with a large drizzle of oil, salt, and pepper. Roast until tender and lightly browned at the edges, about 15 minutes. Drizzle with honey and return to oven until caramelized and golden brown, 5-7 minutes more.

While carrots roast, pat steak dry with paper towels; season all over with salt and pepper. Heat a large 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. Turn off heat; transfer to a cutting board to rest for 5 minutes. Wipe out pan.

Add demi-glace and 1/4 cup water to same pan. Stir over low heat until slightly reduced, 1-2 minutes. Add garlic herb butter and any resting juices from steak. Stir until butter has melted. Turn off heat; season with salt and pepper.

Mash potatoes with a potato masher or fork until smooth. Reserve 1 TBSP chives; stir rest into mashed potatoes with sour cream and 2 TBSP plain butter. Season with salt and pepper.

Slice steak. Divide carrots, potatoes, and steak between plates. Spoon sauce over potatoes and steak. Sprinkle carrots with chili flakes (to taste). Garnish the plate with reserved chives.