1 pound boneless, skinless chicken breast, trimmed and cut into bite-size pieces
½ teaspoon salt, divided
½ teaspoon ground pepper, divided, plus more for garnish
2 tablespoons extra-virgin olive oil, divided
4 cups bite-size broccoli florets
2 tablespoons water
½ cup heavy cream
2 tablespoons white-wine vinegar
2 tablespoons mayonnaise
1 teaspoon cornstarch
½ teaspoon onion powder
½ teaspoon garlic powder
¼ cup chopped mixed fresh herbs (chives, dill, tarragon, basil)