Let chicken breasts sit at room temperature for 15 minutes, then pat dry with paper towels. Drizzle with olive oil and rub evenly with the combined garlic powder, salt, pepper, and paprika on both sides.
Preheat grill or grill pan over medium-high heat, lightly oil the surface, then cook chicken for 6–7 minutes per side until it reaches an internal temperature of 165°F. Rest for 5–10 minutes, then slice against the grain into 1/2-inch strips.
Preheat oven to 375°F and toss bread cubes with olive oil, minced garlic, salt, and pepper, then spread in a single layer on a parchment-lined baking sheet. Bake for 10–12 minutes, stirring once halfway, until golden and crispy; cool completely.
Pulse garlic and anchovies in a food processor until a paste forms, then add egg yolks, lemon juice, and Dijon mustard and blend until smooth. With the processor running, slowly drizzle in olive oil over 2–3 minutes, then add Parmesan and Worcestershire sauce, blend, and season to taste.
Rinse romaine leaves thoroughly under cold water, spin or pat completely dry, then tear or chop into 2–3 inch pieces and place in a large salad bowl.
Toss romaine with half the dressing and half the Parmesan until well coated, adding more dressing as needed, then fold in croutons. Top with sliced chicken, remaining Parmesan, and freshly cracked black pepper; serve immediately.