Preheat the oven: Heat to 475°F (245°C).
If you have a pizza stone, place it in the oven now. A hot surface helps you get a crisp crust.
Prep the dough: Let the dough rest at room temperature for 20–30 minutes so it’s easier to stretch. Lightly flour your surface, then press and stretch the dough into a 12–14 inch round.
Move it to a parchment-lined baking sheet or a floured peel if using a stone.
Parbake for crispness: Brush the dough lightly with olive oil and poke a few holes with a fork to prevent bubbles. Bake for 5–7 minutes until it just starts to set and lightly color.
Add the base toppings: Sprinkle the parbaked crust with mozzarella and 2 tablespoons Parmesan. Add the cooked chicken in an even layer.
Crack some black pepper over the top and add a light pinch of salt.
Bake until bubbly: Return to the oven for 6–9 minutes, or until the cheese is melted, edges are golden, and the bottom is crisp. If using a stone, slide the pizza directly onto it for extra color.
Make the dressing: While the pizza bakes, whisk yogurt, olive oil, lemon juice, Dijon, Worcestershire, anchovy paste or capers, garlic, and Parmesan. Season with a pinch of salt and pepper.
Thin with a teaspoon of water if needed; it should be spoonable, not runny.
Toss the salad: In a large bowl, combine romaine, cherry tomatoes, and red onion. Add about half the dressing and toss gently until the leaves are glossy. Save the rest of the dressing for drizzling.
Assemble: Remove the hot pizza and let it sit 2 minutes.
Pile the dressed salad on top, leaving a small border. Scatter the croutons, add a final shower of Parmesan, and finish with lemon zest and a squeeze of lemon juice.
Serve: Drizzle with remaining dressing and a little olive oil if you like. Slice and serve right away so the lettuce stays crisp.