Sweet Oriental rice, also known as "sticky rice," is essential to the success of the recipe.
Rinse rice under cold water, then soak for 4 hours. Drain and spread on a baking sheet lined with a dish towel.
Coarsely chop chicken and pork in a food processor. Set aside. In a small saute pan over medium-high heat, cook mushrooms in sesame oil until soft, about 5 minutes. Set aside to cool.
Combine chicken, pork, and mushrooms with remaining ingredients, except rice, in a large bowl. Pinch off bits of the mixture and roll into 1-inch balls. Roll balls in soaked rice to coat completely. Place on a baking sheet lined with parchment or waxed paper. Chill for at least 1 hour. (You can also refrigerate for up to a day or freeze, tightly wrapped in plastic wrap, until ready to cook.)
Set bamboo steamer in a wok and add enough water to come to within 1 inch of the bottom of the steamer. Bring to a boil, place rice balls on the steamer rack 1 inch apart, cover, and steam for 30 minutes. Serve hot.