In a large sauté pan, melt the butter and 1 tbsp olive oil. Add the mushrooms and sauté over medium-high heat until browned. Move mushrooms to a bowl.
In the same pan, heat an additional 1 tbsp olive oil over medium heat, then add leeks, shallots, and garlic. Season with salt and pepper, and sauté until mixture has softened, about 4 minutes.
Still over medium heat, add mushrooms to leek mixture, then mix in thyme and tarragon. Sprinkle the entire mixture with flour, and stir to combine, coating all ingredients. Let cook for 1 minute.
Add chicken stock, stir to combine, and cook over medium heat until the sauce has thickened.
Just before serving, add cooked pasta, fontina cheese, and half of Parmesan to mushroom mixture in the pan. Serve with remaining Parmesan cheese.