Preheat the oven to 425 degrees F.
Place the veal and tomato paste into a deep, oven-proof stock pot. Drizzle with 1/4 cup of olive oil and season with salt and pepper. Place in the oven to roast for 30 minutes. Add the rutabaga, carrots, celery, onion, and 3 sprigs of the thyme to the pan. Continue to roast for 20 minutes. Remove from the oven and place over a medium flame. Pour in the wine and enough water to cover by 3 inches. Let simmer for 1 1/2 hours, skim any impurities that rise to the surface.
When reduced by half, remove and strain through a fine sieve. Discard the solids and keep the sauce warm. Season with salt and freshly ground pepper to taste.
Meanwhile, heat the butter and 1/4 cup of the olive oil together in a large saute pan over a low flame. Add the leeks and 2 sprigs thyme to the pan and let soften for 5 minutes. Add the cream to the leeks and continue to cook until thick, about 10 more minutes. Stir occasionally. Season with salt and pepper and set aside to cool.
Use a sharp knife to split the fish open like a book, making a slice in the salmon fillet lengthwise from collar to tail about halfway between the skin and the bottom, being careful not to slice completely through the opposite side. Open the salmon like a book with the skin side down on the cutting board. Season the inside and outside of the fish with sea salt and freshly ground black pepper and begin stuffing the salmon. Spread the leek mixture evenly over the fish. Then begin rolling the flesh side in towards the skin side like a jellyroll. The salmon should roll up until the skin covers the outside of the fish again. Secure with kitchen string in several places and coat the skin with extra virgin olive oil.
Drizzle the remaining olive oil into a large roasting pan and heat over a medium-high flame. Place the salmon in the pan and sear the skin until crispy on all sides, rolling several times in the pan. Carefully place the roasting pan in the oven and roast for five minutes. Slice into 2-inch pinwheels.
While the fish is roasting, start the mushrooms. Pour the remaining olive oil into a large saute pan over a medium flame. Add the shallots, remaining sprig of thyme, and mushrooms. Let the mushrooms cook for 10 minutes, until they release their moisture. Stir often and let the moisture evaporate. Add 3/4 cup of the sauce. Let simmer until the mushrooms absorb the sauce and then season with salt and pepper. Serve the mushrooms with a pinwheel of salmon and additional sauce.