Remove stems and hollow out mushroom caps reserving stems for filling. Season hollowed out caps with olive oil and salt. Small dice stems and pieces.
Fry breadcrumbs in olive oil over med heat until golden brown, stirring constantly. Transfer to a stand mixer.
In the same pan, melt butter, add mushroom stems and salt. When they have started to lose their water, add diced onion, and minced garlic. Sauté until softened.
Let it cool for 5 minutes, then add cream cheese, parm, parsley, pepper, salt, and dried thyme. Mix by hand or stand mixer until homogeneous.
Stuff mushroom caps with filling, pressing fillign into cap. Place on parchment lined sheet tray, top with grated Parmesan, and bake at 425°F/220°C for 25-28 minutes or until mushrooms are tender and golden brown. Larger mushrooms will need a longer roast time to fully cook.