In a small bowl whisk together the lemon zest, lemon juice, mustard and sugar. Slowly whisk in the olive oil in a steady stream until an emulsion is formed. Season with salt and pepper. The vinaigrette can be made ahead of time and kept refrigerated in an airtight container for up to a week.
For the pizza:
Preheat oven to 500ºF (260ºC) with pizza stone set on a middle rack. Once the dough has risen, punch it down and turn it out onto a lightly floured surface. Divide the dough into two equal sections. Roll out the first into a 10" circle and place on a sheet of parchment paper.
Drizzle two tablespoons of the olive oil over the pizza and 1 clove of the minced garlic. Rub the olive oil and garlic over the pizza from edge to edge. Spread a handful of the onions over the pizza. Slide the pizza crust on the parchment paper onto pizza peel and use it to move the pizza to the pizza stone.
Bake the crust for 5 minutes until the edges start to lightly brown. Remove from the oven and sprinkle a cup of the mozzarella cheese over the pizza.
Return the pizza to the pizza stone and continue to cook for another 7 minutes, until the crust is golden brown and the cheese is bubbly and lightly browned. Remove the pizza from the oven and set aside.
Heat oven to broil. Arrange slices of prosciutto on a baking sheet in an even single layer and broil until crispy, about 1 minute.
In a large mixing bowl add the lettuce and toss with 3 tablespoons of the lemon vinaigrette. Add the tomatoes, cucumber and Pecorino Romano, then toss to combine.
Use tongs to top the pizza with ½ of the salad mixture. Arrange sliced avocados all over the top followed by chives. Crumble half prosciutto over the top.
Repeat with the remaining pizza dough, so you have 2 salad-topped pizzas.