Grilled Caesar Salad

Name: Grilled Caesar Salad
Ingredients: 3 tablespoons mayonnaise; 2 tablespoons Worcestershire sauce; 2 lemons, halved, plus 1 tablespoon fresh lemon juice; 1 tablespoon Dijon mustard; 1 teaspoon red wine vinegar; 2 cloves garlic, minced; 3/4 cup extra-virgin olive oil, plus more for grilling; 1/4 cup freshly grated Parmesan; Kosher salt and freshly ground black pepper; 2 hearts romaine lettuce, cut in half lengthwise; Three 3/4-inch slices rustic bread, such as levain or baguette; 1 tablespoon sugar