In a small bowl, whisk together the soy sauce, cornstarch, minced garlic, and grated ginger to create the stir fry sauce. Set aside.
Heat 1 tablespoon of vegetable oil in a large wok or skillet over medium-high heat until glistening.
Add the sliced chicken breasts in a single layer. Cook for 4 to 5 minutes, stirring occasionally, until browned and cooked through. Remove the chicken from the pan and set aside on a plate.
Add the remaining 1 tablespoon of oil to the wok. Add the broccoli, red bell pepper, yellow bell pepper, and yellow onion. Stir fry for 3 to 4 minutes until the vegetables are crisp-tender.
Return the cooked chicken to the wok. Give the stir fry sauce a quick stir, then pour it over the chicken and vegetables.
Toss everything together continuously for 1 to 2 minutes until the sauce has thickened and evenly coated the ingredients.
Remove from heat and garnish with sliced green onions and toasted sesame seeds. Serve immediately over warm rice.