Whisk together the sauce: combine 1/3 cup water, 1/4 cup soy sauce, 2 tablespoons rice vinegar, 2 tablespoons light brown sugar, 1 teaspoon fish sauce, and 1 teaspoon sriracha in a small bowl; set aside.
Bring a large pot of water to a boil and cook the 8 oz pad thai rice noodles for about 4 minutes until tender; drain and rinse under cold water, then set aside.
Heat a large high-sided skillet or wok over medium heat and add 1 tablespoon olive oil.
Toast the cashews: add 1/2 cup roasted salted cashews to the skillet and cook, stirring, for 2–3 minutes until golden; transfer to a plate and set aside.
Add the remaining 1 tablespoon olive oil to the skillet and heat for about 1 minute.
Cook the chicken and vegetables: add the 18 oz thinly sliced chicken, 1/2 thinly sliced sweet onion, and 2 diced large carrots; cook, stirring occasionally, about 5 minutes until chicken is cooked through and vegetables are just tender.
Add the minced garlic and cook, stirring, for 1 minute until fragrant.
Add the sauce and drained noodles to the skillet and toss to combine, cooking about 1 minute to warm through and coat the noodles.
Stir in 1 cup snow peas and 1/4 cup thinly sliced green onion and cook 1 more minute until the snow peas are warmed but still crisp.
Serve immediately topped with the toasted cashews and additional sesame seeds if desired.
