Cook, stirring, in a large skillet over medium-high heat until no longer pink, about 10 minutes:
Tilt the skillet and spoon out all but 2 tablespoons of fat. Add:
Cook, stirring, until the onion is translucent and the juices released by the mushrooms have mostly evaporated, about 10 minutes. Set aside. Proceed as for:
using the sausage-mushroom mixture for the filling and shredded Swiss or Cheddar for the cheese.