Rinse the quinoa under cold water and then cook it according to package instructions, usually about 15 minutes. Set aside once done.
In a large skillet over medium-high heat, add the sesame oil. Once hot, add the minced garlic and grated ginger; sauté for about 30 seconds until fragrant.
Add the diced chicken to the skillet, seasoning with salt and pepper. Cook for about 5-7 minutes or until the chicken is browned and cooked through.
Stir in the broccoli florets, carrots, and red bell pepper to the skillet. Cook for another 5 minutes, stirring occasionally, until the vegetables are just tender but still crisp.
Drizzle the soy sauce over the chicken and vegetables, stirring to coat evenly. Remove from heat.
To assemble the bowls, divide the cooked quinoa evenly among bowls and top with the chicken and broccoli mixture.
Garnish with sliced green onions and a sprinkle of sesame seeds.