Heat the olive oil in heavy, large skillet over high heat. Sprinkle the beef with salt and pepper. Sear the beef in the skillet for 3 to 4 minutes on each side. Remove from the skillet and let rest.
Add the butter and mushrooms to the same skillet and saute until the mushrooms are browned, about 4 minutes. Then, add the shallots, garlic and thyme, and saute for 2 minutes. Add the Beef Reduction to the mushrooms and bring to a boil. Reduce the heat to medium-high and simmer until slightly thickened, about 5 minutes. Add the asparagus and parsley. Season with salt and pepper.
Divide the Lobster Mashed Potatoes among 4 plates. Arrange the beef fillets on the top of the potatoes. Spoon the mushroom and asparagus ragout over the beef and serve.
Preheat the oven to 450 degrees F.
Brush a heavy, large roasting pan with olive oil. Place the shank pieces in the prepared pan. Scatter the carrots and onions around the shanks. Roast until the meat is brown, about 25 minutes.
Transfer the meat and vegetables to a heavy, large saucepan. Place the roasting pan over medium heat. Add the red wine and stir 1 minute, scraping up any browned bits, and then add to the meat and vegetables. Add the beef broth, 4 cups water and thyme sprigs. Bring to a boil, reduce the heat to medium and simmer until the liquid is reduced to 2 cups, about 3 hours.
Strain the broth. Chill uncovered until cool, then cover and keep chilled.
Cook the lobster in a large saucepan of boiling salted water until just opaque in the center, about 7 minutes. Transfer the lobster to a work surface and cool slightly. Remove the lobster meat from the shell. Cut the meat into 1-inch pieces.
Bring 1/3 cup milk to a simmer in a medium saucepan. Add the lobster meat and set aside.
Add the potatoes to a large pot of cold, salted water and bring to a boil. Cook until the potatoes are tender, about 20 minutes. Drain the potatoes, return to the pot and mash. Add the butter and the remaining milk. Mix together well. Add the lobster mixture to the mashed potatoes. Season the potatoes with salt and pepper.