Preheat oven to 400 degrees.
Prep 9 x 13 inch baking dish with non-stick baking spray.
Cut the stems from each mushroom. Set aside. Melt the butter in a saucepan on medium heat.
Chop the stems into fine pieces.
Add the stems and the minced green onions in the saucepan, cooking for about 3 minutes.
Remove the saucepan from the stove.
Add lemon juice, crabmeat, breadcrumbs, eggs, dill, thyme, and ½ cup of cheese. Stir to combine all of the ingredients.
Add 3 tablespoons of melted unsalted butter to the baking dish. Arrange the mushrooms, caps down, in the buttered baking dish.
With a spoon, cover the mushrooms with butter. Flip the caps over, positioning the empty part of the mushroom up.
Stuff the mushroom with the crabmeat mixture. Sprinkle the remaining cheese on top.
Pour the wine around the base of the mushrooms. (Do not cover the mushrooms.)
Bake at 400 degrees until the cheese has melted or 15-20 minutes.