Preheat your oven to 375°F (190°C).
Remove the stems from each portobello mushroom cap and scrape out the gills.
In a large mixing bowl, combine lump crabmeat, panko crumbs, chopped sweet onion, minced garlic, fresh thyme leaves, lemon juice, half of the shredded cheese, and lightly beaten egg. Season with salt and pepper and mix well.
Stuff the mushroom caps with the crab filling, pressing down slightly. Top with remaining shredded cheese.
Place stuffed mushrooms on a baking sheet and bake for about 25 minutes or until golden brown.
Allow to cool slightly before serving with lemon wedges.