Prep. 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. Mix together the crushed tomatoes, gochujang paste, olive oil, minced garlic, toasted sesame oil, salt, and sugar in a bowl.
Saute mushrooms. 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.
Roll out dough. 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.
Prepare pizza. 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. Bake in the preheated oven for 7-10 minutes and then put under the broiler for an additional 2-3 minutes (if needed) until the crust is golden brown.
Garnish. Top with toasted sesame seeds and more sliced green onions if desired.