It may be called Wild Mushroom Pizza, but don't worry — all of the mushrooms in this recipe are easily found in most grocery stores these days. Cremini, shiitake, button, and oyster mushrooms are cooked separately to account for their different cooking times and textures.
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Clean each of the different types of mushrooms separately using a dry brush or towel. Keeping them separate, cut the creminis in half without trimming the stems. Remove the stems from the oyster and shitake mushrooms and cut in quarters.
Heat the oil in a large sauté or cast-iron pan over high heat and be careful not to overcrowd the pan. Sauté the cremini mushrooms until golden brown and caramelized. Add one-fourth of the thyme and rosemary and season with salt and pepper, to taste. Repeat with each variety of mushrooms. Combine the mushrooms when cool.
Preheat the oven to 400 degrees and place a pizza stone or baking sheet inside.
Lightly flour a work surface and roll out the dough to the desired size. Drizzle the olive oil on top and top with ¼ cup of the mushrooms. Top with the pecorino and provolone cheeses. Bake the pizza until golden brown and crispy, about 8-10 minutes. Scatter the diced tomato over the top and garnish with the chopped parsley.