As needed, prep the toppings: shred the mozzarella block and tear the fresh mozzarella into small chunks, grate Parmesan, slice the precooked sausage, cherry tomatoes and olives, and drain and thinly slice the artichoke hearts.
Preheat your BBQ to high, and place your pizza stone in the center. Allow 15 minutes for the stone to come up to temperature.
Remove dough from bowl, and slice into quarters. Return 3 quarters to the bowl, and begin working your first pie from the quarter, stretching and forming to a roughly even circle around 13-15" across.
Lightly dust your pizza peel with flour, and place your dough in the center, jerking slightly to make sure it will be able to slide off onto your stone.
Spoon about 1/4th cup of sauce in the center, using the back of a spoon to evenly spread across the dough, leaving the outside 1/3rd-1/2" exposed.
Add a few of your toppings of choice, then use a food brush to paint olive oil atop the exposed ring of dough. Generously season the whole pie, and especially the exposed crust, with either/both Everything But The Pizza Seasoning and/or Everything But The Garlic Bread Seasoning.
Open the lid to the BBQ, and in a series of small jerking motions, slide the pizza off of the peel and onto the ceramic stone.
Quickly lower the lid, and cook for 3 minutes.
Open the lid, and slide peel under the pizza, removing to a serving board or similar. Garnish with a sprinkle of fresh Parmesan and a few leaves of fresh basil.
Slice up the pizza and pass around, and have fun deciding how to top the next one!