In a large skillet, heat the olive oil over medium heat. Add the oyster mushrooms, shiitakes, beech mushrooms and half of the button mushrooms and cook, stirring, until they release their liquid. Season with thyme and salt. Remove the mushrooms from the pot.
Dice the remaining button mushrooms.
Return the pot to medium-low heat with another 2 tablespoons of oil and the diced button mushrooms. Cook until they've released all of their liquid. Add the garlic and shallots and cook for 5-7 minutes, until softened. Add the sage and brandy, scraping up any browned bits stuck to the bottom of the pot. Bring to a simmer, then stir in the butter and flour.
Cook for 10-12 minutes over medium heat. Add the vegetable stock and heavy cream and return to a boil. Reduce to a simmer and cook until thickened. Stir in the cheeses. If you like you can purée the sauce for a totally smooth consistency.
Fold in the reserved seared mushrooms. Season to taste.
Bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions. Drain the pasta, return to the pot, and drizzle with olive oil.
Toss the pasta with the mushroom sauce and divide between plates. Top with pine nuts and parmesan if you like.