Adjust rack to top position and preheat oven to 425 degrees. Wash and dry all produce. Dice potatoes into 1/2-inch pieces (no need to peel). If necessary, cut broccoli florets into 1-inch pieces. Mince chives.

Place potatoes in a large pot with enough salted water to cover by 2 inches. Bring to a boil and cook until very tender, 15-20 minutes. Reserve 1/2 cup potato cooking liquid, then drain. Return potatoes to pot and add sour cream, half the chives, and 1 TBSP butter (2 TBSP for 4 servings). Mash, adding splashes of reserved cooking liquid as needed, until smooth and creamy; season with salt and pepper. Cover to keep warm.

While potatoes cook, toss broccoli on a baking sheet with a large drizzle of olive oil, salt, and pepper. Roast, tossing halfway through, until browned and slightly crispy, 15-20 minutes.

Meanwhile, pat beef dry with paper towels; season all over with salt and pepper. Heat a drizzle of oil in a large pan over medium-high heat. Add beef and cook until a crust begins to form, 4-7 minutes per side. Remove from heat; set beef aside to rest. Wipe out pan.

Add half the vinegar (use the rest however you like), demi-glace, and 1/4 cup water (1/3 cup for 4 servings) to same pan over medium-high heat. Bring to a simmer and cook until thickened, 2-3 minutes. Remove from heat and stir in 1 TBSP butter (2 TBSP for 4) until melted. Season with salt and pepper.

Divide beef, broccoli, and potatoes between plates. Drizzle beef with sauce. Garnish with remaining chives.