Slice large mushrooms into strips, about 1/2 inch wide. Small mushrooms can be quartered.
In a large pan or skillet set on medium-high heat, melt 2 tablespoons of butter and add the mushrooms. Sautee for a few minutes until mushrooms soften, shrink and become aromatic. Do this in batches if needed until all the mushrooms are softened.
Strip the leaves off 5 sprigs of thyme and add them to the mushrooms. Sautee for 2 minutes.
Add the shallots and garlic. Sautee for 2-3 minutes.
Deglaze with the white wine, scraping any bits stuck to the bottom of the pan. Add the cream, lower the heat to low and simmer for 2 minutes.
The sauce should be ready. Taste and adjust the seasoning to your liking.
Cook the pasta per package instructions, making sure to reserve some of the pasta water. Once ready, carefully transfer the cooked pasta to the pan with the mushroom sauce. Toss to combine. If you feel the sauce is a little thin, add pasta water. Note: this is not a saucy pasta dish.
Plate the pasta and garnish with fresh chopped parsley and freshly grated Parmigiano Reggiano.