Peel and chop the Yukon gold potatoes into uniform pieces. In a large pot, bring water to a boil and add the potatoes. Cook for about 15 minutes or until they are fork-tender. Drain the potatoes, return them to the pot, and mash them with butter, cream, salt, and pepper until smooth and creamy. Keep warm while you prepare the rest of the dish.

Season the filet mignon generously with salt and pepper on both sides. Heat olive oil in a skillet over medium-high heat until it shimmers, about 2 minutes. Sear the steak for 3-4 minutes on each side for medium-rare, until a rich brown crust forms. Use a meat thermometer to check for an internal temperature of 135°F. Remove the steak from the skillet and let it rest for 5-10 minutes.

Preheat your oven to 425°F (220°C). While the steak rests, toss chopped root vegetables in a bowl with olive oil, salt, and pepper. Spread them out on a baking sheet in a single layer. Roast the vegetables in the oven for about 20-25 minutes, stirring halfway through, until they are tender and slightly caramelized.

In the same skillet used for the steak, add a bit more olive oil if needed, then sauté finely chopped garlic and shallots over medium heat for 2-3 minutes until fragrant. Pour in the red wine, scraping the bottom of the skillet to deglaze it. Allow the mixture to simmer and reduce by half, about 5-7 minutes. Stir in Worcestershire sauce.

On warm plates, create a bed of creamy mashed potatoes. Slice the rested filet mignon and place it atop the mashed potatoes. Generously arrange the roasted root vegetables around the steak. Drizzle the red wine reduction over the steak and potatoes.