Melt 2 tablespoons butter in a skillet; cook and stir green onion until softened, about 2 minutes. Transfer green onion to a bowl. Stir in crabmeat, bread crumbs, 1/4 cup Monterey Jack cheese, egg, lemon juice, and dill weed until well mixed.
Pour 1/2 cup melted butter in a 9x13-inch baking dish; turn mushroom caps in butter to coat. Fill mushroom caps with the crab mixture and sprinkle with remaining 1/2 cup Monterey Jack cheese. Pour white wine into baking dish.
Bake in preheated oven until cheese is melted and lightly brown, 15 to 20 minutes.
you will see the bottom of the mushroom leak