Clean mushrooms, then remove stems. I like to give the stems a twist, and they loosen up to remove them, or you can use a knife.
Finely chop mushroom stems and set aside.
Add a small drizzle of oil to a large skillet and heat over MED HIGH heat. Once skillet is hot, add sausage. Cook, crumbling with a wooden spoon or potato masher, for about 4-5 minutes, or until cooked through and finely crumbled.
Use a slotted spoon to remove sausage to a plate. Then reduce heat to MED LOW.
In the same skillet, with the sausage drippings, add onion and garlic and cook, stirring often, for about 3 minutes.
Pour in wine, using a wooden spoon to loosen any browned bits from the bottom of the pan, cooking a few minutes, until most of the wine is reduced and cooked off.
Add chopped mushroom stems, salt, pepper and thyme and cook for 1-2 minutes. Remove to the plate with the sausage and let cool a little.
In a mixing bowl, add softened cream cheese, egg yolk, and Parmesan cheese. Stir well to combine.
Stir in sausage mixture from the plate and make sure it’s well combined.
Cover bowl and refrigerate for about 1 hour. This helps firm the filling up so it doesn't run all over the mushrooms.
Preheat oven to 350°F and line a rimmed baking sheet with parchment paper or foil.
Use a small spoon (or even a teaspoon measuring spoon) to fill mushrooms with the cream cheese mixture, pressing gently to fill the cavity. Add a little more to create a small mound on top of the mushroom.
Repeat with remaining mushrooms. Bake for 25 minutes, or until golden brown. I like to broil mine for a minute or so at the end of baking to make sure the filling is nice and golden.
Let cool 5-10 minutes, sprinkle with minced parsley (if using), and serve.