Preheat the oven to 375°F (190°C). Line a baking sheet with parchment paper or lightly grease it.
Gently clean the mushroom caps with a damp cloth and remove the stems. Place the caps, open side up, on the baking sheet.
In a mixing bowl, combine the cream cheese, crab meat, chopped green onions, minced garlic, Worcestershire sauce, soy sauce, sesame oil, lemon juice, and half of the mozzarella cheese. Mix until smooth and well combined. Season with salt and pepper to taste.
Using a spoon, carefully fill each mushroom cap with the crab mixture, mounding it slightly on top.
Sprinkle the remaining mozzarella cheese over the stuffed mushrooms.
Lightly brush the tops of the mushrooms with olive oil to promote browning while baking.
Bake in the preheated oven for 20 minutes, or until the mushrooms are tender and the cheese is bubbly and golden brown.
Remove from the oven and let cool slightly before serving.