Chicken Caesar Salad Skewers

Name: Chicken Caesar Salad Skewers
Ingredients: 12 (10 to 12-inch) skewers; 1/4 cup grated Parmesan cheese (about 1 ounce), plus more for serving; 4 oil-packed anchovy fillets; 1 clove garlic; 1/2 medium lemon; 1 large egg yolk; 1 teaspoon Dijon mustard; 2 1/4 teaspoons kosher salt, divided, plus more as needed; 1/4 teaspoon freshly ground black pepper; 1/3 cup plus 1 tablespoon canola oil, divided; 1/2 cup extra-virgin olive oil, divided; 2 large romaine lettuce hearts (7 to 10 ounces each); 8 ounces uncut crusty sourdough bread; 1 pound boneless, skinless chicken breasts