To prepare rolls, combine mushrooms and boiling water to cover in a bowl; cover and let stand 10 minutes. Drain and thinly slice mushrooms. Heat vegetable oil in a small nonstick skillet over medium-high heat. Add mushrooms, ginger, and garlic; stir-fry 2 minutes. Remove from heat.
Combine the mushroom mixture, bok choy, carrot, bean sprouts, green onions, and sesame seeds in a large bowl; set aside.
Add cold water to a large, shallow dish to a depth of 1 inch. Place 1 rice paper sheet in dish of water. Let stand 2 minutes or until soft. Place rice paper sheet on a flat surface. Spoon about 1/3 cup vegetable mixture in center of sheet. Fold sides of sheet over filling, and roll up jelly-roll fashion. Gently press seam to seal; place, seam side down, on a serving platter (cover to keep from drying). Repeat procedure with remaining rice paper and vegetable mixture. Slice each roll in half crosswise.
To prepare sauce, combine hoisin sauce and remaining ingredients in a small bowl. Serve with rolls.