Place a large pot of salted water over high heat and bring it to a boil.
Place a large skillet over medium-heat with the EVOO and butter. Add the mushrooms to the pan and cook until golden brown, 6-7 minutes.
Add the onions and cook until tender, 5-6 minutes. Sprinkle the flour into the pan, stir it into the veggies and cook about 30 seconds. Slowly whisk the chicken stock, milk and Dijon mustard into the pan, letting each liquid thicken up before adding the next. Season with salt and freshly ground black pepper, and cook another minute until it has thickened up. Don't worry if it's a little loose, we'll be adding more stuff to it later on.