Preheat the oven to 425°. Unpackage Amy’s frozen Vegan Margherita Pizza and sprinkle 1 cup of plant-based mozzarella shreds on top of the frozen pizza. Place the pizza on a baking sheet or pizza stone and bake for 15 minutes.
While the pizza is baking, in a medium-sized pan, heat 1 tablespoon of olive oil. Add shallots and paprika and cook over medium -ow to medium heat, stirring occasionally, until caramelized, about 10 minutes. Take care not to burn the shallots toward the end. Remove caramelized shallots and set aside.
Add 1 tablespoon of olive oil to the same warm pan. Add 2 cups of shiitake mushrooms, sliced ¼ thick and cook over medium-high heat. Once you add them to the pan, let them sit, without stirring, until browned, about 3 minutes. Turn, and cook until the mushrooms are brown and soft, stirring occasionally, another 3-5 minutes, or until your liking. Remove and set aside.
Remove the pizza from the oven and let it cool. Scatter caramelized shallots first. Place the mushrooms on top of the shallots. To finish, sprinkle the chopped rosemary and red pepper flakes.