Preheat the oven to 400°F.
Lightly grease a baking tray or use parchment paper.
Rinse the mushrooms and dry well. Remove the stems and set aside.
Arrange the mushroom caps on the baking tray.
Chop the mushrooms stems, parsley, and mince the garlic cloves.
In a small frying pan, heat the olive oil and add the chopped mushrooms stems. Fry for about 2 minutes, then add the minced garlic, and continue frying for about 5 minutes. Remove from heat and season with salt and pepper. Transfer to a medium bowl and let them cool.
Add the cream cheese, feta cheese, chopped parsley, thyme, and cayenne pepper to the mushrooms stem mixture and combine well to create the filling.
Place the breadcrumbs in a small pile. Spoon the filling into the mushroom caps, and then dip each mushroom in the breadcrumbs and place it back on the baking tray.
Bake for 20 minutes until the mushrooms are cooked and the breadcrumbs on top are golden. Serve and enjoy.