1. To make the wild mushroom pizza, preheat the oven to 250C, place the pizza base on a baking sheet and pre-bake the pizza crust for about 10 minutes until the outside just begins to brown. Remove it and let it cool and prepare the topping.
2. Prepare the mushroom pizza. In a pan on the stove, over low-medium heat, add the sliced onions and cook until they become caramelized - this will take about 30 minutes. Ensure to stir the onions occasionally and do not let them burn.
3. Next, prepare the mushroom topping. In a large pan on the stove over medium-high heat, add the butter and olive oil. When hot add the shallots and garlic and fry for about 30 seconds. Next, add the mushrooms and wine. Continue stirring until all the liquid has evaporated and add rosemary towards the end, as well as salt and pepper to taste.
4. Brush the pizza base with the garlic oil. Then top with mozzarella, mushrooms, onions and parmigiano reggiano cheese.
5. Bake for about 10 minutes, until the cheese begins to slightly brown. Remove from the oven, let it cool a bit, then slice the pizza and serve.