Cook the rice according to the package directions.
Meanwhile, in a large bowl, combine the chicken, scallions, and ginger. Shape into 16 meatballs.
Heat 1 tablespoon of the oil in a skillet over medium-high heat. Cook the meatballs, turning, until cooked through, 10 to 12 minutes. Transfer to a plate.
Wipe out the skillet. Heat the remaining oil over medium-high heat. Add the peas and edamame. Cook, tossing, for 2 minutes. Return the meatballs to the skillet.
In a bowl, combine the soy sauce and sugar. Add to the skillet and simmer until slightly thickened, 2 to 3 minutes.
Serve the meatballs, vegetables, and sauce over rice.