Carefully remove the stems from the mushrooms. Finely chop the stems and set the caps aside.
In a medium skillet, heat 1 teaspoon of the olive oil over medium heat. Add the onion and chopped mushrooms and cook until tender, about 5 minutes. Add the garlic and cook for one more minute. Remove from heat.
In a medium bowl, combine the panko, Parmesan, parsley, thyme, lemon zest, salt, and red pepper flakes. Stir in the cooked mushroom mixture.
Spoon the filling into the mushroom caps and place the mushrooms on the prepared baking sheet, cavity side up. Drizzle the remaining olive oil over the mushrooms.
Bake for 20 to 25 minutes or until the mushrooms are tender tops are golden. Remove from the oven and serve warm.