Preheat the oven to 400°F. Pour the avocado oil into your cast iron skillet and heat up on medium-high heat until the oil is warmed through. Remove from the heat and add 2 Tbsp parmesan "cheese".
Layer on the broccoli and tomatoes. Then layer on the scallions and peppers.
Next, layer on the mushroom slices and then the spinach.
Finally sprinkle the mozzarella "cheese" all over the top in an even layer.
Drop 3-4 dollops of pizza sauce onto the top of the cheese, and spread them together to make an even layer of sauce, leaving about a 1-2" margin of uncovered cheese around the perimeter.
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.
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.
Sprinkle the remaining Tbsp of parmesan "cheese" over the top of the pizza and return it to the oven for an additional 15-20 minutes. Remove from the oven. Transfer the pizza onto a cutting board and let cool for 5-10 minutes before slicing. Serve hot.