Heat grill to medium-high heat (350° to 400°). Combine first 9 ingredients and 2 tablespoons thyme in a heavy saucepan over medium heat. Cook 20 minutes or until thickened to a saucy consistency, stirring often and breaking up peaches with the back of a spoon. Let cool completely.
Sprinkle semolina flour evenly over a large, rimless baking sheet. Place pizza dough on baking sheet, and pat into 4 (6- to 7-inch) circles.
Brush grill grates with oil, and slide pizza dough onto grates. Grill, covered with grill lid, 2 minutes or until grill marks appear. Slide baking sheet under dough on grill, and reduce heat to medium. Spread dough evenly with peach chutney, leaving a 3/4-inch border. Top with prosciutto, onion, and goat cheese. Grill, covered with grill lid, 8 minutes or until cheese melts and crusts are lightly browned.
Remove pizzas from grill, and sprinkle with black pepper. Brush edges of crusts with 1/2 tablespoon oil. Combine arugula and remaining 1 tablespoon oil in a bowl; toss gently to coat. Top pizza with arugula. Serve immediately.