In bowl, cover rice with 8 cups cold water. Soak at least 1 hour or as long as overnight. In another bowl, soak mushrooms in water 20 minutes until soft and spongy. Drain thoroughly, remove and discard stems; chop finely. In food processor, finely mince green onions and ginger. Add pork, eggs, soy sauce, salt and stock. Process, pulsing on and off until thoroughly combined. (Do not overprocess to a paste.) Transfer to bowl. Mix in mushrooms and water chestnuts by hand, stirring in one direction. (Note: Pork mixture can be prepared, covered closely with plastic wrap and refrigerated up to 24 hours in advance. Mix gently before shaping.)
Rinse rice until water runs clear; drain thoroughly and spread on sheet pan. Form pork mixture into balls with 1 tablespoon scoop. Drop each ball into rice and gently roll to cover completely. Arrange balls in oiled steamer, placing 1 inch apart.
Place over boiling water and steam over medium-high heat 1 1/2 to 2 hours, adding water as needed. (For best texture, steam no less than 1 1/2 hours.) Steamed Pork and Rice Dumplings can be held in steamer over low heat 1 to 2 hours.
For each serving, to order: Plate 1 tablespoon Garlic-Soy Sauce. Top with 3 Steamed Pork and Rice Dumplings. Sprinkle with 1 1/2 teaspoons each minced carrots and minced cilantro.
To make Garlic-Soy Sauce: In bowl, mix 1 cup soy sauce, 1/2 cup distilled white vinegar, 2 1/2 teaspoons oriental sesame oil, 1 scant teaspoon sugar and 3/4 ounce finely chopped garlic. (Makes about 1 1/2 cups.)