First, get all your ingredients together and find yourself a large heavy based frying pan – you’ll need it to be around 10 in. Preheat your grill to maximum.
Slice the red onion and put it into the frying pan with a little oil. Tear the mushrooms into pieces and roughly chop the garlic, then add to the pan with the thyme leaves and cook for 4–5 minutes, turning every so often, until the mushrooms are charred and crispy and cooked through. Remove and put aside for later.
Next, make the cashew ricotta: put all the ingredients into the bowl of a food processor with 3 tablespoons of cold water and blend until completely smooth – this should take 2–5 minutes, depending on how powerful your machine is. It should be the consistency of normal ricotta. Scoop out into a bowl and wash the processor bowl.
Now make the dough. Put the flour and water into the processor with a good pinch of salt and a tablespoon of olive oil and pulse until the dough comes together in a ball. Tip it out and bring it together in your hands.
Get your frying pan on a medium to high heat. If you have two pans about the right size you can do both the pizzas at once, otherwise you can do one after the other, as they cook quickly.
Cut the dough into two equal halves and cover one half for later.
Put the other half on to a floured work surface and use a rolling pin to roll it out into a 1cm thick circle about the size of your frying pan.
Drizzle a little oil into the hot pan, then carefully lift in the dough. Leave it on the heat for about 3 minutes, so the base is starting to cook, while you quickly top the pizza.
Spoon half the tomato puree over, then the mushrooms. Dot with the cashew cheese and the olives.
Pop the pizza under the grill for 4–5 minutes, until it is cooked through and the cashew cheese is browned.
Repeat with the second pizza.
To finish, strew with some arugula leaves and cut into generous slices.
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