Prepare the pizza dough as instructed on the package, or add a drizzle of olive oil and a bit of honey to make it even more supple (amounts included in ingredients below.) The pizza dough kit makes enough dough for 2 pizzas, so save the extra dough for another use or double the amount of ingredients to make 2 pies.
Prepare the pizza dough according to the kit directions. Add a drizzle of olive oil and honey if desired. Knead the dough for 2-3 minutes and place in a lightly oiled bowl, cover with plastic wrap, and place in a spot away from drafts to rise until at least doubled in size, about 30 minutes to 1 hour. The dough can be refrigerated for up to 3 days where it will slowly rise.
Bring the dough to room temperature before shaping and place on a pizza pan.
Drain the mushrooms reserving the sunflower oil. Drizzle half of the oil on the pizza dough then top with the shredded cheese. Tear pieces of the fresh mozzarella cheese and place on pizza then top with mushroom pieces.
Preheat the oven to 450 degrees F. Bake the pizza for 10-12 minutes or until the crust is golden and the cheese is melted and bubbling.
Remove the pizza and sprinkle with red chile flakes.
Toss the arugula with the remaining tablespoon of olive oil, season with kosher salt and freshly ground black pepper and Parmesan cheese shavings. Cut the pizza and top with the arugula and serve.