Preheat oven to 400°F or 205°C.
Clean the mushrooms by wiping clean with a damp paper towel. If very dirty, wash it under running water just briefly, as mushrooms can absorb water and become soggy. Separate the mushroom cap and stem.
In a food processor, add pumpkin seeds and nutritional yeast. Pulse a few times until a rough mixture forms—you want some larger pieces for the crunch. Alternatively, chop the nuts by hand and mix with the nutritional yeast. Transfer to a bowl and set aside. (Optional: reserve 1-2 tablespoons for garnish).
In the same food processor, add mushroom stems, onion, garlic, and dried thyme. Blend to a coarse texture, just before it becomes a paste. Alternatively, chop everything by hand finely.
In a pan, heat olive oil over medium heat. Add the mushroom stem, onion, garlic, and thyme mixture and sauté until fragrant and any liquid has evaporated, about 5-7 minutes. Then add the chopped pumpkin seeds and nutritional yeast mixture and sauté for 1-2 minutes until nuts are toasted. Season to taste with salt and pepper.
Allow mixture to cool slightly, then add mayonnaise and stir until the mixture becomes more cohesive.
Place mushroom caps on a baking dish and drizzle olive oil over top. Flip over so the hollow side faces up and fill each mushroom with the filling until it forms a mound. Optionally sprinkle your reserved pumpkin seed-nutritional yeast mixture as topping.
Place in the oven and bake for 20-25 minutes or until golden brown. Garnish with parsley and enjoy!