Place pizza stone in oven then preheat it to 500°F.
If making your own pizza dough, start that process so the dough can be rising while you're caramelizing the onions.
Heat large skillet and 2 TBSP olive oil on medium. Add onions and separate them. Cover with lid and let sweat for about 10 minutes. Remove lid, add salt and stir occasionally until they turn medium brown. Don't let them stick to the pan and don't burn them. You can add a little balsamic vinegar near the end of the caramelizing.
Add 1 TBSP olive oil in another skillet and sauté mushrooms while onions are caramelizing to save time.
Sprinkle your pizza peel with a little cornmeal to prevent it from sticking.
Lightly flour your countertop. Divide your dough in half and shape it on your counter with your hands or rolling pin until it's about 1/8" thick.
Spread 1 TBSP olive oil on crust, then place half of the caramelized onions, half the duck, half of the mushrooms and half of the cheese on your pizza.
Drizzle with BBQ sauce and pop it the oven for about 8 minutes. Check the crust and make sure it's not burning on the bottom.
Carefully slide pizza onto a cutting board and make second pizza. Sometimes I like to add micro-greens or arugula to pizza after it comes out of the oven.