Halve, destone and peel the avocados. Weigh the flesh – you want 200g to get your ratios right (if you don’t have enough, simply top up to 200g with extra virgin olive oil). In a large bowl, smash up the avo, then gradually rub in the flour, a pinch of sea salt and 4 tablespoons of cold water until you have a dough. Knead until smooth, then wrap and rest for 15 minutes. For the filling, crack the eggs into a blender, then add the frozen peas and most of the Cheddar. Rip in the top leafy half of the basil, add a pinch of salt and black pepper, and blitz until smooth.
Preheat the oven to 200°C/400°F/gas 6. Roll out the avocado pastry on a flour-dusted surface to just under ½cm thick. Loosely roll it up around the rolling pin, then unroll it over an oiled 25cm x 35cm baking tray, ease it into the sides and prick the base. Roughly tear off any big bits of overhang, then bake for 10 minutes, or until lightly golden. Evenly pour in the filling and bake for another 15 minutes, or until set, then finely grate over the remaining cheese. Dress the salad leaves with extra virgin olive oil and lemon juice, season, then sprinkle over the quiche to serve.