Preheat your oven to 500°F (260°C) and place a pizza stone (or an inverted rimmed baking sheet) on the middle oven rack.
Make the sauce by mixing together the crushed tomatoes, gochujang paste, crushed garlic, olive oil, toasted sesame oil, salt, and sugar in a bowl.
Cook the sliced mushrooms in a skillet over medium heat with 1-2 teaspoons of olive oil for about 3-5 minutes This helps prevent them from drying out in the oven.
On a lightly floured surface, roll out your pizza dough into a circular shape and then transfer it to a floured (or use cornmeal) pizza peel or baking sheet.
Spoon a thin layer of the sauce onto the dough (about ¼ - ⅓ cup), leaving about ½-inch space around the edges. Follow with the shredded cheese and the rest of your toppings.
Bake for about 7-10 minutes and then put under the broiler for an additional 2-3 minutes until the crust is golden brown.
Top with toasted sesame seeds (optional) and more sliced green onions if desired.