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1
Heat 1 teaspoon of the oil in a large (PFOA-free) nonstick skillet over medium-high heat. Add the mushrooms, shallot, rosemary, pepper, and (if using) salt and saute until the mushrooms are just wilted, about 6 minutes. Transfer to a bowl and set aside.
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2
Prepare an outdoor or indoor grill, or a grill pan.
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3
Divide the dough into two (7-ounce) balls. Rub the dough balls with the remaining 1 1/2 teaspoons oil. Stretch then shape by hand on a large cutting board into two approximately 9-inch round thin crusts. (Note: It's okay if not perfectly round.)
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4
Gently lay the dough on the grill grates over direct medium heat and grill for 5 minutes, then grill over medium-high heat until the bottom has well-defined, charred grill marks, about 5 minutes. Flip over, top each crust immediately with the mushrooms and cheese, cover, and grill over medium-high heat for 2 minutes; rotate (to form cross-hatch grill marks), and continue to grill, covered, until the crust bottom is browned, dough is cooked through, and cheese is melted, about 2 minutes more. (Note: Grill in batches, if necessary.)
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5
Transfer the pizzas to a cutting board. Slice each in half or into quarters, sprinkle with the parsley, and serve.
