Prepare Crust (if not using store-bought): Place the flour in a bowl with a pinch of sea salt, and gradually pour in up to 150ml/5fl.oz of cold water, using a fork to stir as you go so it comes together into a ball of dough. Knead for just 1 minute on a clean flour-dusted surface, and put aside.
Prepare Pizza Filling: Place a 30cm/12in frying pan on a medium-high heat with 1 tablespoon of olive oil. Peel and finely slice the onion and deseed and finely slice the pepper, adding to the pan as you go, then season with a pinch of sea salt and black pepper. Place a lid on top and fry for 2 minutes, or until golden, tossing occasionally.
Prepare Dough: Meanwhile, roll out the dough into a round the size of the pan (just under ½cm/¼inch thick).
Transfer Dough to Pan: When the time’s up on the veggies, tip them onto your board, then gently transfer the dough to the dry pan, gently pressing in your fingertips into the dough to create dimples. Cover with a lid and cook for 3 minutes on one side, then carefully flip over.
Add Pizza Toppings: Drain away some of the liquid from the tomatoes, then mash lightly with a fork and spread over the dough, leaving a 1cm/⅓inch gap around the edges. Scatter over the cooked veg and coarsely grate over the cheese (it’s nice to get a little over the edge, because as the cheese melts you’ll get a gorgeous gnarly crust). Turn the heat down to medium, put the lid on and cook for a final 3 to 4 minutes, or until the cheese has melted and the base is crispy.
Prepare Salad: Meanwhile, shred the outer leaves of the lettuce, finely slice the stalk, and click apart the inner leaves. Trim and speed-peel the carrot, dress with 1 tablespoon each of red wine vinegar and olive oil, and toss together.
Serve: Slide the pizza on to a board, then slice and serve with the salad.