In a bowl, combine glutinous rice and enough water to cover. Soak for at at least 6 hours or overnight for best results. In a colander, drain well and transfer into a wide plate.
In a small bowl with warm water, soak shitake mushrooms until softened. Using hands, squeeze liquid and then mince.
In a bowl, combine ground pork, water chestnuts, mushrooms, ginger, green onions, garlic, soy sauce, wine, sesame oil, egg, salt, and pepper. Stir to combine.
Form meat mixture into balls of about 1-inch diameter. Gently roll each ball in rice to fully coat, pressing rice onto the meat.
Line a steamer with banana leaves Chinese cabbage leaves, or parchment paper. Arrange rice-coated meatballs in a single layer on steamer at about 1/2 inch apart.
Steam for about 20 to 30 minutes or until rice and meat are cooked through. Serve with dipping sauce.