Bring a large pot of salted water to a boil and cook the pasta for 1 minute longer than package directions. Drain, rinse with cold water, and let cool.
Rub chicken breasts with vegetable oil, season with salt, pepper, and paprika. Sear in a large skillet over medium-high heat until deeply golden and internal temperature reaches 165°F, about 5-7 minutes per side.
Prepare the Caesar dressing by whisking together oil, garlic, anchovy filets (if using), capers, lemon juice, mustard, Worcestershire sauce, salt, and pepper until well combined and smooth. Whisk in mayonnaise until well combined, then whisk in grated parmesan and whole milk.
Combine the cooled pasta, diced chicken, sliced romaine lettuce, croutons, and parmesan cheese in a large bowl.
Pour the prepared Caesar dressing over the pasta mixture and toss until everything is well coated.
Serve immediately and enjoy!