Preheat the oven to 400˚. Place a pizza stone, steel, or an upside-down baking sheet on the upper third rack of the oven. 

Place the cauliflower in the center of a lint free kitchen towel. Pull the four sides up to make a bundle and squeeze very well over the sink to remove as much moisture as possible.

Combine the dried cauliflower, cream cheese, 1/4 cup of parmesan, egg, 1 grated garlic clove, 1 teaspoon of salt, 1/2 teaspoon ground black pepper, and Italian seasoning in a medium bowl until well combined.

Place a 14-inch piece of parchment paper on a half-sheet pan. Pour 2 tablespoons of the oil onto the parchment and dust with the cornmeal. Place the cauliflower mixture onto the prepared parchment. Gently pat the crust into a 12-inch round.

Transfer the half sheet pan to the preheated baking stone. Bake until the crust is golden and dried out, 20 to 25 minutes. Remove to a wire rack.

Melt the butter in a medium sauté pan over medium heat. Add the mushrooms and cook, stirring frequently until the liquid reduces and the mushrooms begin to brown. Stir in the thyme, 1 grated garlic clove, 1/2 teaspoon salt, and 1/4 teaspoon pepper and stir until mushrooms are golden brown. Stir in the balsamic vinegar and allow the vinegar to reduce slightly, about 30 seconds. Remove the mushrooms from the heat.

Combine the ricotta, 2 tablespoons parsley, remaining grated garlic clove, 1/4 teaspoon of salt, and 1/4 teaspoon of pepper in a medium bowl. 

Brush the surface of the cauliflower crust with the remaining 1 tablespoon of olive oil and sprinkle with the remaining 1 tablespoon of parmesan. Sprinkle the mozzarella all over. Dot the surface with the ricotta mixture. Top with the mushrooms. Bake until the cheese is melted and bubbly, 12 to 14 minutes more.