Combine chicken thighs and 1 tablespoon of oil in a large bowl. Add the remaining ingredients and stir until evenly coated.
Heat a very large sauté pan over medium-high heat for 2 minutes. Add the remaining tablespoon of oil and heat for 1 minute. Place chicken in the pan in a single layer, avoiding overcrowding. Cook for approximately 3 minutes per side until golden brown and crisp. Remove chicken with a slotted spoon and set aside.
Add onions and a large pinch of kosher salt to the pan. Cook over medium-high heat for 2 minutes, stirring occasionally. Add bell peppers, broccoli, carrots, sugar snap peas, and the white parts of the green onions. Cook for 5 to 7 minutes until fork-tender, covering with a lid and stirring occasionally. Stir in the water chestnuts halfway through the cooking time.
Whisk all sauce ingredients together in a small bowl. Pour the sauce into the stir-fry and reduce heat to medium-low. Cook for 2 to 3 minutes, stirring frequently.
Return the chicken to the pan and add sesame oil and red chili pepper flakes. Cook for approximately 2 minutes, stirring to allow the flavors to meld.
Adjust seasoning to taste and serve with cauliflower or white rice. Garnish with scallions, the green parts of the green onions, and sesame seeds.
