Preheat oven to 425°F (220°C). Generously grease 12 muffin tins. Heat oil in large skillet over medium heat. Add mushrooms and onion; cook until mushrooms start to brown, about 8 min. Season with salt. Cool completely.
Meanwhile, on lightly floured work surface, roll out pizza dough to 15 x 11-in. (38 x 28-cm) rectangle, approx. 1/4-in. (5-mm) thick. Spread 1/2 cup (125 mL) tomato sauce on top, leaving 1/2-in. (1-cm) border. Sprinkle on 2/3 cup (150 mL) mozzarella cheese. Scatter mushroom mixture, prosciutto and basil over top. Starting from one long end, roll up tightly into log shape, pinching ends to seal. Cut into 12 equal pieces.
Place one piece into each prepared muffin tin, cut-side up. Spoon remaining sauce on top and sprinkle with remaining mozzarella cheese. Bake 15 to 20 min. or until golden brown and bubbling. Sprinkle with Parmesan. Serve warm.
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