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Step 1
Adjust rack to top position and preheat oven to 425 degrees. Wash and dry all produce. Cut potatoes into ½-inch-thick wedges. Trim green beans, if necessary. Halve, peel, and mince shallot until you have 2 TBSP. Place peppercorns in a zip-close bag; crush with a rolling pin or a heavy pan. Thinly slice chives.
Step 2
Toss potatoes on a baking sheet with a large drizzle of oil and a large pinch of salt and pepper. Roast on top rack until lightly browned, about 15 minutes (we’ll add more to the sheet then).
Step 3
Once potatoes have roasted 15 minutes, remove baking sheet from oven. (For 4 servings, leave potatoes roasting and add green beans to a second sheet.) Carefully push potatoes to one side. Carefully toss green beans on opposite side of sheet with a drizzle of oil and a pinch of salt and pepper. Continue roasting until veggies are browned and tender, 10-15 minutes.
Step 4
Meanwhile, pat beef dry with paper towels; season all over with salt and pepper. Heat a drizzle of oil in a medium pan over medium-high heat. Add beef and cook to desired doneness, 3-6 minutes per side. Turn off heat; transfer to a plate and let rest for 5 minutes. Wash out pan.
Step 5
Melt 1 TBSP butter in same pan over medium heat. Add minced shallot and cook, stirring, until slightly softened, 1-2 minutes. Add demi-glace, ¼ cup water (⅓ cup for 4 servings), and 1 tsp crushed peppercorns (be sure to measure). Simmer until slightly thickened, 1-2 minutes. Turn off heat. Stir in another 1 TBSP butter (2 TBSP for 4), half the chives, and any resting juices from beef. Season with salt and more peppercorns, if desired.
Step 6
Divide potatoes, green beans, and beef between plates. Top beef with sauce. Sprinkle with remaining chives.