Boil the eggs for nine minutes, then plunge into cold water to cool.
Half-fill a deep, heavy-based pan with the vegetable oil and heat until a breadcrumb sizzles and turns brown when dropped into it. (CAUTION: Hot oil can be dangerous. Do not leave unattended.)
Heat the oil and butter in a frying pan. When the butter is foaming add the onion, carrot, garlic and chilli flakes and fry until the onion is softened.
Place the chickpea purée into a bowl. Add the fried ingredients and mix well.
Add the beetroot and thyme and season very well with salt and freshly ground white pepper.
Peel the eggs then dredge them in the flour.
Wrap the mix chickpea mixture around each of the boiled eggs, making sure there are no gaps and mould into balls.
Roll the coated eggs in the beaten egg, then roll in the breadcrumbs to coat completely.
Carefully add the coated eggs to the hot oil and deep-fry for 3-4 minutes, or until crisp and golden-brown. Remove with a slotted spoon and drain on kitchen paper.
Serve the veggie scotch eggs with a good dollop of piccalilli.