Heat the oven to 400°F and line a baking sheet with parchment paper. The pan will be ready when the filled mushrooms are assembled, which keeps the process quick and tidy.
Clean the mushrooms by wiping them with a damp paper towel, then remove the stems and place the caps on the prepared baking sheet. The caps should look clean and dry, not wet, which helps them bake up with better texture.
Chop the reserved mushroom stems very finely. Small pieces blend into the filling more evenly and keep it thick rather than chunky.
Melt the butter in a medium skillet over medium-high heat, then add the chopped stems and cook for about 5 minutes. They should soften and give off their moisture, and the pan will smell rich and earthy.
Stir in the garlic and thyme, cook for 1 minute, then add the cream cheese, half of the parmesan cheese, salt, and pepper. The garlic should smell fragrant right away, and the mixture should loosen as the cheese warms.
Take the skillet off the heat once the filling is smooth, then stir in most of the parsley and save the rest for serving. The finished filling should look thick and scoopable, not runny.
Let the filling cool briefly, transfer it to a ziptop or piping bag, and pipe it into each mushroom cap. A slightly cooled filling holds its shape better and stays neatly mounded in the mushrooms.
Sprinkle the tops with the remaining parmesan cheese and bake for about 15 minutes. The tops should be golden brown, and the mushrooms will have just started to soften and release their liquid.
Finish with the reserved parsley, if desired, and serve warm. The fresh herbs add a little color and brighten the rich, cheesy filling.