Place oven rack in lowest position. Heat oven to 425°F.
Coat a 15 x 10 x 2-inch jelly-roll pan with nonstick cooking spray. Stretch pizza dough to fit pan; place in pan. Brush dough with half the olive oil; sprinkle with salt and pepper.
Bake dough on bottom rack in 425°F oven for 7 minutes.
Remove pan from oven. Leave oven on. Sprinkle focaccia with prosciutto. Dry tomato slices slightly on paper towels; arrange over dough, overlapping, if necessary. Sprinkle with crumbled cheese. Top with rosemary. Drizzle with remaining oil.
Bake in 425°F oven until cheese is softened and tomatoes and crust are browned, 9 to 10 minutes. Cool slightly. Serve warm or at room temperature.