Heat the oven to 375 °F. A fully heated oven helps the thin chicken mixture begin setting when it goes in.
Cover a baking sheet with parchment paper. The paper provides a release surface for the cheese-rich crust.
Pulse the drained, rinsed chicken, egg, Parmesan, garlic powder, and crushed red pepper flakes together in a food processor. Stop when the ingredients form a cohesive, slightly tacky mixture without separate pockets of egg or cheese.
Move the mixture onto the lined sheet and use clean hands, lightly oiled if needed, to shape a circle about 1/4 inch thick. An even layer prevents a thick, soft middle surrounded by overly thin edges.
Bake for 40 to 45 minutes, checking for a golden-brown surface and a firm center. The crust should feel set across the middle rather than soft or spongy.
Take the baking sheet out and let the crust cool for 5 minutes. Allowing the strongest heat to subside helps the lettuce stay crisp after assembly.
During the crust's baking time, blend the Greek yogurt, lemon juice, anchovy, garlic, Parmesan, and black pepper. The finished dressing should look creamy and smooth, with no visible garlic or anchovy pieces.
Wash and chop the romaine, then place it in a bowl with the salad Parmesan and dressing. Well-drained leaves keep the dressing creamy rather than watery.
Turn the salad gently until the dressing coats the chopped leaves. Aim for an even coating throughout, including the crunchy rib pieces at the bottom of the bowl.
Distribute the dressed salad over the slightly cooled chicken crust. Spread the topping across the surface rather than leaving one heavy mound in the center.
Finish with additional Parmesan and ground black pepper if desired, then serve. The finished pizza should combine a firm savory crust with cool, crunchy greens.