In a large skillet, heat the vegetable oil over medium-high heat. Add the minced garlic and grated ginger, sautéing for about 30 seconds until fragrant.
Add the ground chicken to the skillet, breaking it apart with a spatula. Cook for about 5-7 minutes, or until the chicken is fully cooked and no longer pink. Season with salt and pepper.
While the chicken is cooking, steam the broccoli florets until bright green and tender, about 3-4 minutes. You can do this in a microwave-safe bowl with a splash of water covered with a plate.
In a small bowl, whisk together the honey, Sriracha, soy sauce, and sesame oil.
Once the chicken is cooked, add the steamed broccoli to the skillet. Pour the honey Sriracha sauce over the chicken and broccoli, stirring to combine. Cook for an additional 2-3 minutes until everything is heated through.
Serve the honey Sriracha ground chicken and broccoli over cooked rice or quinoa if desired.