To prepare meatballs, heat a small skillet over medium-high heat. Add oil to pan; swirl to coat. Add mushrooms, 1 tablespoon minced ginger, and 1 tablespoon garlic; sauté 2 minutes. Add sherry; cook 3 minutes or until liquid evaporates and mushrooms are tender. Remove from heat; cool. Place mushroom mixture and miso in a mini chopper; pulse 10 times or until very finely chopped.
Combine mushroom mixture, remaining 1 1/2 teaspoons minced ginger, remaining 1 1/2 teaspoons garlic, chicken, and next 6 ingredients (through egg white) in a bowl. Shape mixture into 36 (1-inch) meatballs. Thread 3 meatballs onto each of 12 (6-inch) flat bamboo skewers. Chill for 30 minutes.
To prepare sauce, combine mirin, soy sauce, sugar, and vinegar in a small saucepan. Bring to a boil; cook 3 minutes or until slightly thickened. Remove from heat; cool slightly. Stir in juice, 2 teaspoons grated ginger, and serrano. Reserve 2 tablespoons sauce.
Heat a grill pan over medium heat. Coat pan with cooking spray. Place 6 skewers in pan; cook 9 minutes, turning to brown on all sides. Remove from pan; brush half of sauce over meatballs. Repeat procedure with remaining 6 skewers and sauce. Sprinkle with sesame seeds; serve with reserved 2 tablespoons sauce.
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