Wash and dry all produce. Adjust rack to upper position and preheat oven to 425 degrees. Peel carrots, then cut on an angle into 1/2-inch-thick pieces. In a large bowl, whisk together herbs de Provence, half the honey, and 1 TBSP olive oil. Season with plenty of salt and pepper. Add carrots and toss to coat.

Arrange carrots on a baking sheet. Roast in oven until browned and tender, about 20 minutes. Meanwhile, cut potatoes into evenly sized cubes. Place in a medium pot with salted water to cover by 2 inches. Bring to a boil and cook until tender, about 15 minutes. Once done, drain well and set aside.

Meanwhile, trim, then thinly slice scallions, separating greens and whites. Pat steaks dry with a paper towel, then season generously all over with salt and pepper. Heat a large drizzle of oil in a large pan over medium-high heat. Add steaks and cook to desired doneness, 4-6 minutes per side.

Remove steaks from pan and set aside to rest for at least 5 minutes. Wipe out any browned bits from pan with a paper towel. Halve, peel, and mince shallot until you have 2 TBSP. Melt 1 TBSP butter in pan used for steaks over medium heat. Add minced shallot and cook until just softened, about 1 minute. Stir in demi-glace and 1/3 cup water. Simmer until slightly thickened, about 1 minute.

Stir 1 TBSP butter and any juices released by steaks into pan. Remove from heat and season with salt and pepper. Once carrots are done roasting, drizzle with remaining honey and sprinkle with chili flakes to taste. Place pot used for potatoes over low heat. Add 1 TBSP butter and scallion whites. Cook, stirring, until scallions are slightly softened, about 1 minute.

Add potatoes to pot and mash with a potato masher or fork until smooth. Stir in sour cream. Season with salt and pepper. Slice steaks against the grain. Divide carrots, potatoes, and steaks between plates. Spoon pan sauce over steaks and potatoes. Garnish with scallion greens.