Heat oil in a wok or large skillet over medium-high heat. Add garlic and ginger and cook 1 minute. Add chicken and cook 3 to 4 minutes, until starting to brown, stirring constantly. Add onions, carrots, and peppers and cook 1 minute. Add snap peas, corn and broccoli and cook 2 minutes. Add soy sauce and cook 2 minutes, until vegetables are crisp-tender.
Dissolve cornstarch in chicken broth in a small bowl and add to wok. Simmer 2 minutes, until sauce thickens. Serve over rice.