Preheat oven to 425 degrees. Wash and dry all produce. Zest and halve lemon. Thinly slice chives. Place 2 TBSP butter (4 TBSP for 4 servings) in a large microwavesafe bowl; microwave until softened, 10-15 seconds. Stir in lemon zest, half the chives, and half the paprika. Season with salt and pepper; set aside. Dice potatoes into 1/2-inch pieces. Halve, peel, and mince half the shallot (all for 4). Rinse shrimp; pat dry with paper towels. Season with salt, pepper, and remaining paprika.

Place potatoes and garlic cloves in a medium pot with enough salted water to cover by 2 inches. Bring to a boil and cook until potatoes are tender, 15-20 minutes. Reserve 1/2 cup cooking liquid; drain and return potatoes and garlic to pot. Mash with half the crème fraîche (you’ll use the rest later) and 1 TBSP plain butter (2 TBSP for 4) until smooth, adding splashes of reserved cooking liquid as needed. Season with salt and pepper. Keep covered off heat.

While potatoes and garlic cook, toss green beans on a baking sheet with a drizzle of olive oil, salt, and pepper. Place lemon halves cut sides down on same sheet. Roast on top rack until browned and tender, 12-15 minutes total (we’ll add more to the sheet in step 4). Cover with foil to keep warm, if necessary.

Meanwhile, pat steak dry with paper towels. Season all over with salt and pepper. Heat a drizzle of olive oil in a large pan over medium-high heat. Add steak; cook until browned but not yet cooked through, 3-6 minutes per side. Turn off heat; wipe out pan. Transfer steak to sheet with green beans; roast steak to desired doneness, 4-7 minutes. (TIP: If green beans are done first, remove from sheet and continue roasting steak.) Set steak aside to rest.

Heat a drizzle of olive oil in pan used for steak over medium-high heat. Add shrimp; cook until pink and cooked through, 3-4 minutes. Turn off heat. Add to bowl with lemon paprika butter; toss to coat. Cover to keep warm. Wipe out pan; return to medium heat with a drizzle of olive oil. Add shallot; cook 1 minute. Stir in demi-glace, mustard, and 1/4 cup water (1/3 cup for 4); cook until thickened, 1-2 minutes. Turn off heat; stir in remaining crème fraîche. Season with pepper.

Thinly slice steak against the grain. Divide steak, potatoes, and green beans between plates. Top steak with pan sauce and buttery shrimp. Sprinkle with remaining chives. Serve with roasted lemon on the side.