Take one whole chilli and using a small sharp knife make an incision along the length without cutting all the way through. Open up the cavity and using the end of a teaspoon scrape out and discard the seeds and the membrane.
Mix the cream cheese with the mozzarella, season with salt and pepper then use it to fill the chillies. Push them gently to close them up and wipe off any excess.
Put the flour, egg and breadcrumbs in separate shallow bowls or dishes and roll the stuffed chillies first in the flour then egg then breadcrumbs then repeat so they get a good double coating.
Heat the oil in a large saucepan until it reaches 160C. Carefully lower the chillies into the oil using a slotted spoon and deep fry in batches for around 2-3 mins or until deep golden brown. Transfer to a plate lined with kitchen paper to soak up the excess oil.
Once the chillies are fried season them with pepper and salt and spread out on a plate or board so everyone can help themselves.