Prepare the Chicken: Preheat grill or grill pan over medium-high heat. Rub chicken breasts with olive oil, garlic powder, smoked paprika, salt, and pepper. Grill 5–7 minutes per side until cooked through and internal temperature reaches 165°F (75°C). Let rest 5 minutes, then slice.
Make Parmesan Croutons: Preheat oven to 375°F (190°C). Toss bread cubes with olive oil, Parmesan, garlic powder, salt, and pepper. Spread on a baking sheet and bake 8–10 minutes until golden and crispy.
Make the Caesar Dressing: Mash anchovies and garlic into a paste. Whisk in Dijon mustard, lemon juice, Worcestershire sauce, and mayonnaise. Gradually whisk in olive oil until smooth. Stir in Parmesan cheese and season to taste.
Assemble the Salad: In a large bowl, toss romaine lettuce with Caesar dressing. Add sliced grilled chicken and Parmesan croutons. Garnish with extra Parmesan shavings.