Heat a large pan with butter and olive oil over medium-high heat. Add the mushrooms and cook until they have softened, about six to eight minutes. This might have to be done in batches to avoid overcrowding the pan. Add the white and light green parts of the scallions and shallots. Cook until softened, about five minutes.
Sprinkle on the thyme, oregano, black pepper, and flour and mix together until all the vegetables are coated. Pour in the vegetable broth and bring to a simmer. Reduce the heat to low and cook for ten minutes, until the liquid has reduced.
Add the sour cream, goat cheese, and heavy cream and mix together well. Cook until it heats up and thickens slightly, about two to four minutes. Taste and season with salt and additional pepper. Either toss the noodles in the sauce or place a portion on a plate and top with the sauce.