In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the chicken pieces and season with salt and pepper. Cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the garlic and ginger, stirring for about 30 seconds until fragrant. Add the sliced bell peppers and snap peas, cooking for another 3-4 minutes until they are tender-crisp.
While the vegetables are cooking, in a small bowl, whisk together the soy sauce, honey, cornstarch, and water until smooth.
Return the cooked chicken to the skillet and pour the sauce over the chicken and vegetables. Stir well to coat everything in the sauce and cook for an additional 2-3 minutes until the sauce thickens.
Gently fold in the diced mango and drizzle with sesame oil. Cook for another minute to warm the mango through.
Serve the stir-fry over cooked rice or quinoa.