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Make the dough by combining the flour, yeast and salt (don't put the latter two directly on top of each other) then pour in the olive oil and rub it in well. Pour in the water slowly, mixing by hand or with a spatula until you have a shaggy mess (that's the official term). Bring together to a smooth dough, adding water cautiously but with pizza, the wetter the better is the way to go - it should be like a very thick, stiff batter rather than a dough.
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If kneading by hand, knead for 10 minutes and make use of a dough scraper to work the dough. It should be smooth and when gathered into a ball, will flow slightly to take the shape of it's container. If using a stand mixer, 5 minutes should do it but do it on the lowest speed and stop every now and again to scrape the dough down as most domestic mixers can't take this volume of dough and it won't mix thoroughly otherwise.
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Place in a large, oiled bowl and cover with cling film. Allow to prove for up to 24 hours in a cool kitchen. If it is hot, put it in the fridge until needed.
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On a lightly floured surface, take the dough and roll it around from cupped hand to hand until it forms a nice, smooth, taut ball. Place on a sheet of reusable silicone paper (sold as Bake-o-glide in a lot of shops) or baking parchment which you have lightly dusted with flour and then sprinkled with polenta - the latter helps the dough not to stick. Cover with a large upturned bowl and leave the rest for an hour.
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Preheat the oven as hot as it will go (usually about 240˚C in domestic ovens) with a shelf positioned half way down with either a pizza stone, welsh bakestone or a second (heavy duty) baking sheet on the shelf to preheat. We're going to cook hot and fast - it's the best way by far to make pizza in a domestic oven.
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Blitz the canned tomatoes, garlic, parsley, olive oil and a little seasoning with a stick blender or in a food processor and use a third to spread thinly onto the pizza base, leaving 1-2 cm uncovered at the edge. Freeze the rest in a couple of food safe plastic bags for another day.
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Spread with tomato sauce onto base using the back of a spoon to get it evenly distributed.
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Distributed the sliced sausages, mushrooms and cherry tomatoes evenly around the pizza then tuck in little rags of the ham in between. Bare in mind you'll need space for the eggs.. Rip up the mozzarella ball and likewise, distribute around the pizza.
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Now to bake. You are going to scoop the pizza, still on it's silicone/baking parchment onto the metal baking tray without a lip (if yours is lipped, turn it upside down) then shunt it onto the hot bakestone. It's the poor man's version of using a pizza peel! Just be careful when opening the oven door as it is super hot so stand back and do use an oven glove to protect your hand.
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Bake for 10 minutes until almost fully cooked. Meanwhile, crack however many quail's eggs you want into individual pots (believe me, they are fiddly enough to crack - do it now then the oven wont lose too much heat when you top the pizza with the eggs).
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Open the oven door carefully, use a ladle to create enough dips in the partially cooked pizza base as you have eggs and pour them into these shallow depressions. Quickly season with sea salt, black pepper and a little extra parsley then shunt back into the oven to cook for 2 minutes more to set the whites but leave the yolk rich and creamy. Eat immediately!