In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the ground turkey and cook until browned, about 5-7 minutes. Break it apart with a spatula as it cooks. Season with salt and pepper.
Add the sliced onion and bell pepper to the skillet. Stir-fry for about 3-4 minutes until they begin to soften.
Add the broccoli florets, minced garlic, and ginger. Stir-fry for another 3-4 minutes until the broccoli is bright green and tender-crisp.
In a small bowl, whisk together the soy sauce, honey, rice vinegar, sesame oil, and red pepper flakes (if using). Pour the sauce over the stir-fry and mix well. Cook for an additional 2-3 minutes to heat through.
Serve the stir-fry over cooked rice or quinoa.