Start by cleaning the mushrooms gently with a damp paper towel to remove any dirt. Twist out the stems and set the caps aside on a parchment lined baking sheet. Finely chop the stems since they will add extra flavor to the filling.
In a skillet, heat 1 tablespoon of olive oil over medium heat. Add the chopped mushroom stems, shallot, and garlic. Cook until softened and fragrant, about 5 minutes. This step deepens the flavor and ensures the filling has a savory base.
Transfer the cooked mixture to a mixing bowl. Stir in the panko, Parmesan, parsley, thyme, and a pinch of salt and pepper. Add a drizzle of olive oil to help the mixture bind together. You want the filling to be moist enough to hold but not soggy.
Using a small spoon, scoop the breadcrumb mixture into each mushroom cap, pressing lightly so it stays in place. Pile the filling a little higher than the rim of the mushroom since it will shrink slightly as it bakes.
Drizzle the stuffed mushrooms with the remaining olive oil and place the tray in a preheated oven at 400°F (200°C). Bake for 18 to 20 minutes, until the mushrooms are tender and the tops are golden brown.
Remove from the oven and let them cool for a couple of minutes before transferring to a serving platter. If you like, squeeze a little lemon juice over the top for brightness or sprinkle with more parsley for color. Serve warm and watch them disappear quickly.