Preheat the oven to 200C/400F/Gas 6.
For the pizza base, place the flour, oil, water and salt into a food processor and blend together until a dough is formed. Tip out onto a floured work surface and knead. Shape into a round base about 20cm/8in wide.
Place into a frying pan over a high heat and brown the base, then using a mini-blowtorch, crisp the top of the pizza. (Alternatively you can do this under the grill.)
For the topping, spread tomato purée over the top of the base.
Fry the mushrooms in a dry frying pan then scatter over the tomato purée. Arrange the prosciutto and cheese on top.
Crack an egg into the middle, then place into the oven for five minutes to finish cooking.
Serve on a large plate, and slice into wedges to serve.