Love is a many splendored thing, but splendor ain't got nothing on some steak. Specifically, the tender filet mignon, a cut of beef that melts in your mouth. (And will melt your valentine's heart.) The filet gets an assist from a rich, buttery demi-glace sauce that'll have you kissing your plate clean. Rounding out this lovely lover's meal is a delectable Gouda gratin and hearty green beans. Serve this to your special someone, and have a wonderful, romantic Valentine's Day.
Slice potatoes into 1/8" rounds. Bring a medium pot with potatoes and enough lightly salted water to cover to a boil. Reduce to a simmer and cook until softened, 10-12 minutes. While potatoes cook, trim and thinly slice green onions on an angle, keeping white and green portions separate. Cut Gouda into ¼" dice. Trim ends off green beans. Rinse steaks, pat dry, and season both sides with ¼ tsp. salt and a pinch of pepper.
Make the Gratin
Strain potatoes and return to pot over medium-high heat. Add cream and green portions of green onions. Bring to a boil, reduce to a simmer, cover, and cook until slightly thickened, gently stirring occasionally, 5 minutes. Add half the Gouda and season with a pinch of salt and pepper. Transfer potatoes to oven-safe casserole dish, and place dish on baking sheet. Top with remaining Gouda and bake until cheese browns, 15-18 minutes. While potatoes bake, cook steaks.
Cook the Steaks
Place a medium non-stick pan over medium-high heat. Add 1 Tbsp. olive oil and steaks to hot pan and cook until browned and steaks reach a minimum internal temperature of 145 degrees, 5-8 minutes on each side. Remove steaks to a plate, cover with foil, and rest at least 5 minutes. Wipe pan clean and reserve. Remember to always rest cooked meats before serving for juicier results.
Cook the Green Beans
Return pan used to cook steaks to medium-high heat and add ⅓ the butter (reserve remaining for sauce), green beans, and ¼ cup water. Bring to a simmer and cook until bright green and tender, 2-4 minutes. Season to taste with salt and pepper. Transfer green beans to a plate and wipe pan clean.
Make the Bordelaise Sauce
Return pan used to cook green beans to medium heat. Add demi-glace, ½ cup water, and white portions of green onions (reserve a pinch for garnish). Bring to a simmer and cook until just thick enough to coat back of a spoon, 2-3 minutes. Remove from burner, add remaining butter, and swirl to incorporate. For a smoother texture, strain sauce through wire-mesh strainer.
Plate the Dish
Spoon sauce onto plate. Scoop a portion of gratin onto plate. Place a serving of green beans next to potatoes and place steak on top of sauce. Garnish steak with remaining white portions of green onions.