Combine the vegetables in a large bowl – broccoli/cauliflower, carrots, garlic, sweetcorn and parsley.*You can use a mix of cauliflower and broccoli stalks, and you can also swap one of the broccoli/cauliflower stalks for e.g. 1/2 courgette or similar.
Add the Parmesan, sesame seeds, breadcrumbs and one egg, season with salt and pepper, and mix well.Let the mixture stand for a moment until it comes together. Give it a stir and add another egg (or 1/2 egg) if the mixture is too dry. It should be soft and slightly sticky.
Heat a generous glug of oil in a frying pan, then shape the mixture into flat patties. I scoop up a heaped tablespoon of the mixture into my hand and use the spoon to shape it and press it gently flat.
Fry the fritters over a fairly high heat until golden on both sides. Only turn them once the first side has formed a good golden crust.
Set the fritters aside on a piece of baking paper or similar – they crisp up once they have rested for a moment.
Serve with a good dip – tartare sauce, ranch dressing or similar.