In a bowl, toss the cut chicken pieces with 1 tablespoon soy sauce and 1 teaspoon cornstarch. Set aside for 10 minutes.
Heat a wok or large skillet over medium-high heat. Add 1 tablespoon vegetable oil. Add the cashews and toast for 2-3 minutes until lightly browned. Remove cashews and set aside.
Add the marinated chicken to the hot wok. Cook until browned and cooked through, about 5-7 minutes. Remove chicken and set aside.
Add the minced ginger and garlic to the wok. Stir-fry for 30 seconds until fragrant.
Add the snap peas and carrots to the wok. Stir-fry for 2-3 minutes until the vegetables are bright green and slightly tender-crisp.
In a small bowl, whisk together the chicken broth, 2 tablespoons soy sauce, oyster sauce, rice vinegar, sesame oil, brown sugar, and 1 teaspoon cornstarch to create the sauce.
Pour the sauce mixture into the wok with the vegetables. Bring to a simmer, stirring constantly until the sauce thickens.
Return the cooked chicken and the toasted cashews to the wok. Toss everything together until the chicken and vegetables are coated in the sauce. Cook for 1 minute more.
Remove from heat. Garnish with sliced green onion before serving.
Notes
For extra flavor, you can lightly coat the chicken in a little flour before marinating.
To keep the snap peas very crisp, add them in the last minute of stir-frying.