Preheat your oven to 375°F (190°C). Clean the portobello mushroom caps with a damp cloth.
In a mixing bowl, combine crabmeat, panko crumbs, chopped onion, garlic, thyme, lemon juice, half of the cheese, egg, salt, and pepper. Mix thoroughly.
Fill each mushroom cap generously with the crab mixture and top with the remaining cheese.
Place the stuffed mushrooms on a baking sheet lined with parchment paper and bake for about 25 minutes until golden brown.
Remove from the oven, let cool slightly, and serve warm with lemon wedges.