Peel, trim, and cut carrot into sticks, ½"-thick.
Cut potatoes into ¼" rounds.
Trim and thinly slice green onions.
Pat lamb chops dry, and season both sides with ¼ tsp. salt and a pinch of pepper.
Roast the Vegetables
Place carrot and potatoes on prepared baking sheet and toss with 1 Tbsp. olive oil, ¼ tsp. salt, and a pinch of pepper. Massage oil into vegetables.
Spread into a single layer and roast in hot oven until turning brown and tender, 25-30 minutes.
While vegetables roast, cook lamb chops.
Cook the Lamb Chops
Place a medium non-stick pan over medium heat and add 2 tsp. olive oil.
Add lamb chops to hot and cook undisturbed until browned, 5-7 minutes.
Flip chops. Brush with mustard and sprinkle with herbs de provence. Cook until chops reach a minimum internal temperature of 145 degrees, 3-5 minutes.
Flip again and cook undisturbed, 30 seconds.
Remove lamb chops to a plate and rest at least 5 minutes.
Wipe pan clean and reserve.
Make the Sauce
Return pan used to cook lamb chops to medium heat and add ¼ cup water and demi-glace to pan. Stir to combine.
Cook until slightly thickened, 1-2 minutes.
Remove from burner. Swirl in butter.
Finish the Dish
Plate dish as pictured on front of card, garnishing vegetables with goat cheese and green onions. Bon appétit!