In a large skillet, heat the olive oil over medium heat. Add the minced garlic and grated ginger, sautéing for about 1 minute until fragrant.
Add the ground turkey to the skillet, breaking it apart with a spatula. Cook until browned and cooked through, about 5-7 minutes. Season with salt and pepper.
While the turkey is cooking, steam the broccoli florets until tender but still bright green, about 4-5 minutes. You can do this in a steamer basket or in the microwave with a little water.
In a small bowl, whisk together the soy sauce, honey, sriracha, and rice vinegar. Pour this mixture over the cooked turkey and stir to combine. Let it simmer for 2-3 minutes to allow the flavors to meld.
Serve the sweet and spicy turkey mixture over a bed of cooked rice or quinoa, topped with steamed broccoli.