Prepare the Dough (if making from scratch): In warm water, dissolve the sugar and yeast. Let sit until frothy, 5 to 10 minutes. Mix the flour and salt together in a big basin. Add the olive oil and yeast mixture. Mix until a dough forms, then knead for 5–7 minutes until smooth on a floured surface. For around an hour, cover and allow to rise in a warm location.
Make the Alfredo Sauce: In a small saucepan, melt the butter over medium heat. Cook the minced garlic for approximately one minute, or until it becomes aromatic. Bring to a slow simmer after adding the heavy cream. When the sauce is smooth and the Parmesan cheese has melted, add the salt, pepper, and cheese and remove from the fire. Put aside.
Preheat Oven and Prep Crust: Set the oven temperature to 425°F (220°C). On a baking sheet or pizza pan dusted with flour, punch down the rising dough and roll or stretch it into a circle that is 12 to 14 inches in diameter.
Assemble the Pizza: With a 1-inch margin for the pizza dough, evenly cover the crust with Alfredo sauce. Top with the cooked chicken, red onion, and spinach, then the shredded mozzarella cheese (if using).
Bake: Bake for 12 to 18 minutes, or until the cheese is melted and bubbling and the crust is golden brown.
Garnish and Serve: Take out of the oven, top with fresh parsley, cut into slices, and serve right away.