Place a rack in the center of the oven. Preheat the oven to 350 degrees F.
With a paper towel, wipe off the outsides of mushrooms. Remove and finely chop stems. Set the caps aside.
Heat the oil in a large nonstick skillet over medium. Brown the sausage until cooked through, using a sturdy spoon to break apart the meat into small pieces (this will take about 8 minutes).
To the skillet, add the mushroom stems, vinegar, salt, and pepper. Cook until the stems are softened, about 4 minutes.
Stir in the green onion, garlic, and Italian breadcrumbs. Set aside to cool.
In a large bowl, stir together the cream cheese, egg yolk, and Parmesan with a fork until smoothly combined.
Fold in the sausage mixture.
With a spoon, generously fill each mushroom cap so that you create a mound on top. Arrange in a baking dish large enough to hold them snugly in a single layer.
Bake the stuffed mushrooms until browned and the filling is cooked through, about 20 minutes.
Transfer to a serving plate and let cool at least 5 minutes. Sprinkle with fresh parsley. Enjoy warm or at room temperature.
