In a medium saucepan, combine 1/3 cup low-sodium soy sauce, 1 cup water, 2 tablespoons rice vinegar, 2 tablespoons low-carb sweetener, 1 tablespoon hoisin sauce, 2 tablespoons sugar-free ketchup, 2 teaspoons sesame oil, 1 minced garlic clove, and 1/2 teaspoon red chili flakes.
Place the saucepan over medium heat, bring the mixture to a simmer, then reduce heat to low and stir occasionally. Simmer until the sauce is slightly reduced and thickened, about 5–10 minutes.
Remove the sauce from the heat and set it aside while you cook the chicken and broccoli.
Heat 2 tablespoons sesame oil in a large skillet over medium-high heat.
Add the remaining minced garlic clove to the hot oil and sauté for about 30–60 seconds, until fragrant (do not let it burn).
Add 1 pound boneless, skinless chicken thighs (cut into 1" pieces) to the skillet. Season the chicken with 1/4 teaspoon salt and 1/4 teaspoon ground black pepper.
Cook the chicken, stirring occasionally, until browned and cooked through, about 8 minutes.
Add 1 head of broccoli, cut into florets, to the skillet and cook with the chicken for about 3 minutes, until the broccoli is tender-crisp.
Pour the prepared General Tso sauce over the chicken and broccoli in the skillet. Bring to a simmer over medium-low heat and cook for about 5 minutes, stirring occasionally, until everything is heated through and the sauce coats the chicken and broccoli.
Remove the skillet from heat and sprinkle 1/4 cup chopped green onion over the dish. Serve immediately.