Preheat the oven to 375°F.
Arrange the portobello mushrooms on a baking sheet, gill side up. Drizzle with olive oil and season with salt and pepper.
In a mixing bowl, combine the crab meat, cream cheese, mozzarella cheese, Parmesan cheese, mayonnaise, Dijon mustard, lemon juice, garlic powder, Old Bay seasoning, salt, black pepper, and parsley. Mix until well combined.
Spoon the crab mixture evenly into each portobello mushroom cap, pressing down slightly to pack it in.
Bake in the preheated oven for 20-25 minutes, or until the mushrooms are tender and the filling is golden brown on top.
Remove from the oven and let cool for a few minutes before serving.