While the pasta is cooking, heat 4 tablespoons of butter and the olive oil in a large skillet over medium-high heat. Add mushrooms, sprinkle with salt and pepper, and saute until golden brown, making sure the majority of the water has been released, around 5 minutes.
1 pound mushrooms, 6 tablespoons unsalted butter, 1 tablespoon extra virgin olive oil, salt and pepper
Add the shallots and saute until translucent, about another minute. Next, add the garlic, thyme and chili flakes and saute one more minute.
1 medium shallot, 5 garlic cloves, 4 sprigs thyme, ½ teaspoon chili flakes
Turn the heat to high and deglaze the pan with the white wine and chicken stock. Scrape up any brown bits on the bottom of the pan. Let cook until the alcohol has been cooked off, approximately 30 seconds to a minute.
⅓ cup white wine, ¼ cup chicken stock
Return the heat to medium, then pour in the heavy cream, stirring to coat the mushrooms. Pour about ¼ cup of the pasta water into the sauce to thicken. If it’s not thick enough, add a little more of the pasta water at a time, making sure to cook the liquid down to thicken the sauce.
1 cup heavy cream
Once the pasta sauce has thickened, turn off the heat and toss the pasta and the remaining 2 tablespoons of butter into the sauce, stirring until fully melted and incorporated.