Preheat the oven to 400°F. Pour the avocado oil into your skillet and heat up on medium-high heat until the oil is rippling. Add the onions and garlic and cook until fragrant, about 2-3 minutes. Take the onions and garlic out of the skillet and set aside in a small bowl for later.
Arrange the pepperoni in a single layer across the entire bottom of the skillet. Cook until they have flattened against the skillet and are sizzling. Remove from the heat and let cool for 5 minutes.
Sprinkle the parmesan cheese over the pepperoni in an even layer.
Next, layer on the onions and garlic, being careful to spread them evenly around the entire pan.
Do the same with the mushrooms, and then the basil. Sprinkle the oregano evenly over everything.
Next, layer your mozzarella cheese over everything, again in an even layer.
One Tbsp at a time, spoon your pizza sauce in evenly-spaced globs (use more or less sauce depending on personal preference) and then spread the sauce so that it fills in the gaps between where the globs were. Try to avoid spreading the sauce too close to the edges of the pan, leaving about a ½-1" gap.
Roll your pizza dough out so that it's flat. Carefully stretch out your pizza dough by draping it over your knuckles and letting gravity do the rest. Rotate the dough and repeat until the dough is stretched out enough to fit the 12" pan, and use it to cover the contents of the pan. Use your fingers to push the dough down between the pizza toppings and the side of the pan.
Brush the olive oil over the entire top of the dough, and put the skillet into the oven for 25 minutes, or until the dough has browned.
Remove the pan from the oven and place on a trivet or on a bare stovetop. Place a baking sheet on top of the skillet, and with oven mitts (!!), carefully and quickly flip both over, making sure to press the skillet firmly against the baking sheet the entire time. If the pizza doesn't drop perfectly out of the skillet onto the baking sheet, use a spatula to gently coax the pizza out of the skillet.
Rearrange any errant pepperoni slices and then return the pizza to the oven for an additional 15-20 minutes, or until the top is browned. Remove from the oven. Transfer the pizza onto a cutting board and let cool for 5 minutes before slicing. Serve hot.