Preheat your oven to 200°C (400°F). Gently wipe the mushroom caps with a damp cloth and carefully remove the stems, setting them aside for the filling.
Finely chop the mushroom stems. In a small skillet, heat a tablespoon of olive oil over medium heat until it shimmers and starts to smell nutty. Sauté the chopped stems with a pinch of salt until they soften and release a savory aroma, about 3-4 minutes.
Meanwhile, toast the panko breadcrumbs in the skillet until golden brown and crispy, about 2-3 minutes. Remove and set aside to cool slightly.
In a mixing bowl, combine the softened cream cheese, sautéed mushroom stems, toasted breadcrumbs, minced garlic, chopped parsley, thyme, lemon zest, and a pinch of salt and pepper. Mix until smooth and evenly incorporated.
Use a spoon to generously fill each mushroom cap with the prepared mixture, pressing lightly to pack the filling inside.
Arrange the stuffed mushrooms on a baking sheet, cap side up. Lightly brush the tops with olive oil to encourage golden browning.
Bake in the preheated oven until the mushrooms are tender and the tops are golden and bubbling, about 15-20 minutes. The filling should be set and fragrant.
Remove from the oven and let rest for 5 minutes. The filling will firm up slightly, making them easier to serve.
Garnish with extra chopped parsley if desired, and serve warm for a savory, aromatic bite.