Preheat your oven to 500°F (260°C) and place a pizza stone inside on the middle rack (or an inverted rimmed baking sheet).
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 your 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 corn meal) pizza peel or baking sheet.
Spoon about ¼ - ⅓ cup of sauce onto the dough, 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 to encourage browning.
Top with toasted sesame seeds (optional) and more sliced green onions if desired.