1. Prepare the dressing by combining the mayonnaise, Greek yogurt, lemon juice, garlic, Dijon mustard, and anchovy paste in a medium-sized bowl. Season with salt and black pepper, to taste, and whisk to combine.
2. Add grated Parmesan cheese to the dressing and stir to combine. Slowly drizzle the olive oil into the dressing and whisk until thoroughly incorporated into the mixture. Taste and season with additional salt and black pepper, if needed. Cover and refrigerate until ready to use.
3. Place top oven rack in the center position and pre-heat to 400°F. Line a large, rimmed baking sheet with parchment paper or a Silpat™ baking sheet.
4. Arrange the chicken breasts on the prepared baking sheet and sprinkle evenly with the Italian seasoning, garlic powder, salt, and black pepper. Place the baking sheet in the pre-heated oven and roast for 20-25 minutes, or until the chicken is cooked through.
Note: An instant-read thermometer inserted into the thickest part of the chicken should read just over 160°F when it is ready. The temperature will continue to rise several degrees while the chicken rests.
5. Remove chicken from oven and cool for 10-15 minutes before slicing.
6. To serve, assemble the salad by adding the chopped Romaine lettuce to a large mixing bowl. Add the shaved Parmesan and drizzle with 1/3 cup dressing. Gently toss to combine.
7. Divide salad between chilled salad plates and top with the sliced chicken breast. Serve immediately with the remaining salad dressing and additional shaved Parmesan on the side. Enjoy!