Preheat an oven to 375ºF.
Place a large skillet over medium high heat with 2 tablespoons EVOO, about 2 turns of the pan. Add the sausage to the pan and cook, breaking it up with a spoon, until the meat is crumbled and golden brown, about 10 minutes.
Add the mushrooms to the pan and cook until golden brown, 5-6 minutes. Season the mixture with salt and freshly ground black pepper and reserve.
While the meat is browning up, place a large saucepot over medium heat and melt the butter. Sprinkle the flour over the butter and cook it for about 1 minute. Whisk in the milk and chicken stock and bring the sauce up to a bubble. Add in the nutmeg and season it with salt and freshly ground black pepper, then simmer until the sauce thickens, 3-4 minutes.