In a medium bowl, whisk together 2 tablespoons low sodium soy sauce, 2 tablespoons rice vinegar, 1 teaspoon toasted sesame oil, 2 tablespoons oyster sauce, and 1 tablespoon cornstarch until smooth; set the sauce aside.
Heat 2 tablespoons oil in a large wok or skillet over high heat until shimmering.
Season 1 pound chicken thigh strips with 1 teaspoon salt and 1/2 teaspoon black pepper.
Add the chicken to the hot wok and cook until golden and cooked through, about 3 to 4 minutes per side; remove or push to the side of the pan if needed.
Add 1 head broccoli florets, 3 sliced green onions, 1 tablespoon grated ginger, and 3 minced garlic cloves to the pan; stir-fry for about 3 minutes until broccoli is bright and slightly tender.
Pour the reserved sauce over the chicken and vegetables and stir to combine.
Add 1/4 cup low sodium chicken stock (or broth or water) and continue stirring until the sauce thickens and coats the ingredients, about 1 to 2 minutes.
Serve the sesame chicken and broccoli over cooked white or brown rice.