Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the chicken pieces and 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 cashews and toast them for about 2-3 minutes until golden, stirring frequently. Remove and set aside with the chicken.
Add the red bell pepper, broccoli, and snap peas to the skillet. Stir-fry for about 4-5 minutes until the vegetables are tender-crisp.
Stir in the garlic and ginger, cooking for an additional 1 minute until fragrant.
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 vegetables and stir to combine.
Return the chicken and cashews to the skillet, tossing everything together to coat in the sauce. Cook for another 2-3 minutes until heated through.
Serve the stir-fry over cooked rice or quinoa.