Preheat oven to 375°F; prepare baking sheet.
Clean mushrooms, remove stems, chop stems, scoop gills.
Mix cream cheese, Parmesan, panko, stems, garlic, parsley, thyme, salt, and pepper; taste and adjust.
Brush caps with oil, stuff with filling, and place on the sheet.
Bake 20–25 min until golden.
Serve on a white ceramic platter with parsley, wine, and salad.