Season chicken with salt and pepper.
Heat 1/2 tablespoon oil in a large pan over medium heat.
Add the chicken and cook, stirring occasionally, until browned and just cooked through, 5 to 7 minutes. Transfer to a plate.
Add the remaining oil, broccoli and water to the pan.
Cover and cook, stirring occasionally, until tender-crisp, 3 to 4 minutes.
Transfer to the plate with the chicken.
Whisk cream, vinegar, mayonnaise, cornstarch, onion powder, garlic powder and some salt and pepper in a measuring cup.
Increase heat to medium-high and pour the cream mixture into the pan.
Bring to a simmer and cook, stirring, until thickened, about 2 minutes.
Return the chicken and broccoli to the pan and sprinkle with herbs; cook, stirring, until heated through, 1 to 2 minutes more.