Preheat oven to 200°C. Line 2 baking trays with baking paper. Place pizza bases onto prepared trays. Spread each base with 1/4 cup of tomato sauce. Use a knife to score top of each pizza into quarters.
Sprinkle half the cheese over 2 opposite quarters of 1 pizza. Place half the prosciutto onto 1 cheese quarter. Arrange half the tomatoes on the other cheese quarter.
Place half the artichoke quarters onto 1 of remaining quarters. Place half the mushrooms onto final quarter. Repeat with remaining ingredients to prepare second pizza. Bake for 25 minutes, swapping pizzas after 12 minutes, or until cheese has melted and pizza bases are crisp. Sprinkle basil over tomatoes. Sprinkle oregano over mushrooms. Serve.