In a small bowl, stir together chicken stock, soy sauce, brown sugar, 4 teaspoons cornstarch, sriracha, and 1 teaspoon sesame oil. Set aside.
Season chicken with 2 teaspoons salt and pepper; toss with remaining 1 tablespoon cornstarch. Heat a large skillet or wok over medium-high heat; add 3 tablespoons canola oil.
Add chicken and half of garlic and ginger; cook until white but not fully cooked through, about 4 minutes. Remove from skillet; set aside.
Add remaining garlic and ginger to skillet; cook 1 minute. Add remaining 1 teaspoon sesame oil, mushrooms, peppers, broccoli, water chestnuts, and remaining ½ teaspoon salt. Cook until vegetables begin to soften, about 3 minutes.
Return to chicken to skillet; add sauce. Cook, stirring occasionally, until sauce is thickened, about 4 minutes. Serve over rice; garnish with scallions.