Preheat oven to 425 degrees. Wash and dry all produce. Trim and halve Brussels sprouts lengthwise. Mince or grate 1 clove garlic (2 cloves for 4 servings). Zest and halve lemon. Dice potatoes into 1/2-inch pieces (no need to peel); place in a large pot with enough salted water to cover. Bring to a boil and cook until tender, 15-20 minutes. Reserve 1/2 cup potato cooking liquid, then drain.

Melt 1 TBSP butter (2 TBSP for 4 servings) in same pot over low heat. Add minced garlic and cook until fragrant, 30 seconds. Return potatoes to pot; mash with a potato masher until smooth, adding splashes of reserved potato cooking liquid as needed. Stir in sour cream; season with salt and pepper. Keep covered until ready to serve.

Meanwhile, toss Brussels sprouts in a large bowl with a large drizzle of olive oil and a pinch of salt and pepper. Place Brussels sprouts and 1 lemon half (both halves for 4 servings) cut side down on a baking sheet. Roast on top rack until golden brown, 20-25 minutes.

Meanwhile, pat beef dry with paper towels; season generously with salt and pepper. Heat a large drizzle of oil in a large pan over medium-high heat. Add beef and cook to desired doneness, 4-7 minutes per side. Turn off heat; transfer to a cutting board to rest. Wipe out pan.

Melt 1 TBSP butter (2 TBSP for 4 servings) in same pan over medium heat. Add remaining garlic and 1 sprig rosemary (2 sprigs for 4); cook, stirring, until fragrant, 30-60 seconds. Reduce heat to low. Add demi-glace, mustard, and 1/4 cup water (1/3 cup for 4 servings). Cook, stirring, until thoroughly combined, 1-2 minutes. Stir in any resting juices from beef. Turn off heat. Season with salt and pepper. Remove and discard garlic and rosemary.

Slice beef against the grain. Top Brussels sprouts with as much juice from roasted lemon as you like; sprinkle with lemon zest and chili flakes to taste. Divide beef, Brussels sprouts, and mashed potatoes between plates. Spoon sauce over beef and serve.