Cook the penne pasta until al dente according to package directions, drain, and rinse with cold water to stop the cooking process and prevent it from sticking.
While the pasta is cooking, make the dressing by combining the mayo, Greek yogurt, lime juice, shredded parmesan, minced garlic, chopped anchovies, Dijon mustard, and Worcestershire sauce until creamy.
In a medium-sized skillet, heat half a tablespoon of olive oil over medium-high heat and brown the diced chicken breasts until fully cooked, about 3 minutes on each side.
Place the cooked pasta, chopped lettuce, grape tomatoes, cooked chicken, and croutons in a large bowl. Pour in the dressing and toss to combine. Serve with extra parmesan cheese on top.