Preheat the oven to 400°F (200°C). Season the beef coulotte generously with salt and black pepper. In a large oven-safe skillet, heat the olive oil over medium-high heat. Sear the beef on all sides until browned, about 3-4 minutes per side. Transfer the skillet to the preheated oven and roast for 30-35 minutes, until the internal temperature reaches 130°F (54°C) for medium rare. Remove from the oven and let rest for 10 minutes before slicing.

Mushroom Ragu

Cook the Ragu

While the beef is resting, prepare the mushroom ragu. In a large skillet, melt the butter over medium heat. Add the diced shallots and minced garlic, and sauté until translucent, about 3 minutes. Add the mixed mushrooms and thyme; cook until the mushrooms are browned and have released their moisture, about 8-10 minutes. Pour in the red wine and vegetable broth, scraping the bottom of the skillet to deglaze. Simmer until the sauce thickens, about 10 minutes. Season with salt and pepper to taste.

Yorkshire Pudding

Prepare the Yorkshire Pudding Batter

In a bowl, whisk together the flour and salt. In a separate bowl, whisk the eggs and milk until combined. Gradually add the egg mixture to the flour, whisking until smooth. Let the batter rest for 20 minutes. Meanwhile, preheat a muffin tin in the oven with beef drippings or vegetable oil in each cup, about 5 minutes.

Bake the Yorkshire Puddings

Once the batter has rested and the muffin tin is hot, carefully pour the batter into each cup, filling them halfway. Bake for 20-25 minutes or until puffed and golden brown. Do not open the oven door during baking.

Beef Jus

Make the Beef Jus

In a large pot, add the beef bones, onions, carrots, celery, thyme, bay leaves, and water. Bring to a boil over high heat, then reduce to a simmer. Allow it to cook for 3-4 hours, skimming off any foam that rises to the top. Strain the liquid through a fine mesh sieve, discard solids, and return the liquid to the pot. Simmer until reduced to desired thickness, about 30 minutes. Season with salt and pepper.