Charred Broccoli Caesar Salad with Chicken

Name: Charred Broccoli Caesar Salad with Chicken
Ingredients: 6 tablespoons mayonnaise; 1 ounce Parmesan cheese , grated (½ cup), divided, plus extra for serving; 7 tablespoons plus 1 teaspoon extra-virgin olive oil , divided; ½ teaspoon grated lemon zest and 1 tablespoon juice; 2 teaspoons white wine vinegar; 2 teaspoons Worcestershire sauce; 2 teaspoons Dijon mustard; 3 anchovy fillets , rinsed and minced (optional); 1 garlic cloves , minced to paste; ¾ teaspoon plus ⅛ teaspoon pepper , divided; ½ cup panko bread crumbs; ¾ teaspoon plus ⅛ teaspoon table salt , divided; 1 pound boneless, skinless chicken breasts , trimmed; 1¾ pounds broccoli; ½ teaspoon sugar; ⅛ teaspoon red pepper flakes