In a large skillet or wok, heat the vegetable oil 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 minutes until golden brown. Remove and set aside with the chicken.
Add the bell pepper, broccoli, and snap peas to the skillet. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
Add the garlic and ginger to the vegetables and stir-fry for an additional minute until fragrant.
In a small bowl, mix together the soy sauce, oyster sauce, cornstarch, and chicken broth until well combined. Pour this sauce over the vegetables in the skillet.
Return the chicken and cashews to the skillet, stirring to coat everything in the sauce. Cook for another 2-3 minutes until the sauce thickens and everything is heated through.
Remove from heat and garnish with sliced green onions. Serve over cooked white rice.