In a large pot, bring salted water to a boil. Add the cubed potatoes and cook until tender, about 15-20 minutes. Drain the potatoes and return them to the pot. Add butter and milk, then mash until smooth. Season with salt and pepper to taste. Keep warm.

Preheat a grill or grill pan over medium-high heat. Toss the asparagus with olive oil, salt, and pepper. Grill the asparagus for about 5-7 minutes, turning occasionally, until tender and slightly charred. Remove from heat and set aside.

Season the filet mignon steaks generously with salt and pepper. In a large skillet, heat olive oil over medium-high heat. Once hot, add the steaks and sear for 4-5 minutes on each side for medium-rare (adjust time for your preferred doneness). Remove from skillet and let rest for a few minutes.

In the same skillet, reduce heat to medium and add the sliced mushrooms. Sauté until they are browned, about 5 minutes. Stir in the chopped rosemary and cook for another minute. Sprinkle the flour over the mushrooms and stir to combine.

Gradually add the beef broth, stirring constantly to avoid lumps. Bring the mixture to a simmer and cook until thickened, about 3-5 minutes. Stir in butter and season with salt and pepper to taste.

On each plate, place a generous scoop of buttered mash, top with a filet mignon, and drizzle with rosemary mushroom gravy. Arrange the grilled asparagus on the side. Enjoy your delicious meal!