Place a pizza stone in the oven and preheat oven to 500°F. This will take about 30 minutes.
While the oven is preheating, cook the chorizo. Heat a medium skillet over medium-high heat and cook the chorizo, breaking it up into small chunks, until cooked through, about 5 minutes. Remove from pan and place on a paper towel.
Sprinkle a pizza peel lightly with flour and set aside. If you don’t have a pizza peel, you can use the back of a rimmed baking sheet or a rimless baking sheet.
Place the pizza dough on a lightly floured surface. Divide the dough into two equal pieces. Take one of the dough halves and flatten it with your hands. Starting at the center and working outwards, use your fingertips to press the dough to 1/2-inch thick. Turn and stretch the dough until it will not stretch further.
Let the dough relax 5 minutes and then continue to stretch it until it reaches the desired diameter, about 12 inches. Transfer the flattened dough to the prepared pizza peel and reshape if necessary.
Brush the dough with 1 tablespoon olive oil. Spread half of the minced garlic evenly on top of the dough. Add half of the toppings to the dough, the shredded Monterey jack cheese, mozzarella cheese, cooked chorizo, corn kernels, green onions, and jalapeno slices. Once you have the toppings on the pizza dough, you need to move quickly so the pizza is easy to transfer to the oven.
Open the oven and carefully scatter a little cornmeal on the preheated pizza stone. Carefully transfer dough to the hot stone. Bake until the cheese is melted, and the crust is golden brown, about 8 to 12 minutes.
While the first pizza is in the oven, make the second pizza the same way, using the remaining toppings. When the first pizza comes out of the oven, bake the second pizza.
Garnish the pizzas evenly with cotija cheese, cilantro, and avocado slices, if using. Slice and serve!