Preheat the oven to 500 degrees F. Line a baking sheet with parchment paper and lightly brush with oil.
Add the cauliflower florets to a food processor and pulse until the texture of small crumbs. If your food processor is small, you may have to do this in batches. Remove to a microwave safe bowl. Cover the bowl with a plate so no air escapes and microwave the cauliflower for approximately 4 minutes. Use oven mitts to remove the bowl. Let the cauliflower stand uncovered until cool enough to touch. In two batches, transfer the cooked cauliflower crumbs to a clean dish towel. Squeeze out all the moisture possible. The drier the crumbs, the crispier the crust. Transfer the drained crumbs to another bowl. The two batches should both be about the size of a tennis ball.
Mix the cauliflower together with the Parmesan, mozzarella, salt, dried herbs, pepper flakes, and egg until very well incorporated. Form the mixture into a ball and transfer to the making sheet. Top with a second piece of parchment paper and roll out as thin as possible in either a circular pie or a rectangular flatbread. (If you don't have a rolling pin, wine bottles work well!). Bake the crust in the oven until browned around the edges and firm, about 15 - 20 minutes.
Meanwhile, make the topping: heat the olive oil in a large non-stick skillet. Saute the shallot and mushroom over a high flame until tender and beginning to brown, about 5 minutes. Season with salt and set aside.
Spoon the tomato sauce over the prepared cauliflower and spread in an even layer, leaving some room for a crust. Sprinkle with the mozzarella and arrange the mushrooms on top. Return to the oven for 5-10 minutes, until the cheese is beginning to brown.
Cut the pizza into wedges and serve immediately.