Remove pizza dough from refrigerator at least 30 minutes before cooking. Heat grill on medium. Lightly brush clean grill grates with oil.
With floured hands or rolling pin, on large sheet of lightly-floured parchment paper, stretch and roll pizza dough into 13-inch round. Generously brush top of pizza with 2 tablespoons of oil.
Using parchment, place dough, oiled side down, on grill. Remove parchment; cook 2 minutes or until bottom is crisp and charred. Flip dough and top with sauce and 1/2 cup cheese; cover and cook 1 minute, until dough is lightly charred on bottom.
With vegetable peeler, cut zucchini into long, thin slices. In medium bowl, toss zucchini, jalapeño, mint, lemon juice, remaining 2 tablespoons olive oil, 1/2 teaspoon salt and 1/4 teaspoon freshly ground pepper.
Top pizza with zucchini salad, prosciutto and remaining 1/4 cup cheese.