Wash and slice zucchini into 1-inch thick rounds. Scoop out the center with melon baller, trying to remove as much flesh as possible without puncturing the bottom. Set the hollow zucchini on a baking sheet with parchment paper.
Sauté onions in butter until light brown. Add sliced mushrooms, and cook over medium high flame until soft. Add wine, chicken stock, if using, salt, and pepper and cook until liquid is evaporated and set aside.
Whisk eggs and milk until smooth. Fill zucchini with a little mushroom mixture, pine nuts, and fill to top with egg and milk mixture. Top with cheese and bake in a preheated 350 degree F oven for 15 minutes, until the cheese browns.