Put the onions in a pan with the cider vinegar and sugar. Bring to a simmer and cook for 30-35 minutes until the onions are sticky, and lightly caramelised. You can leave them for the first 15 minutes, but after that they’ll need regular stirring. Season well.
Meanwhile, put each chicken breast between 2 sheets of baking paper or cling film (if they’re large, cut them in half widthways first). Using a rolling pin, pound them until they’re about 1cm thick. Put the flour and breadcrumbs on separate plates and lightly beat the eggs in a shallow bowl with some seasoning. Dust each chicken breast/piece in flour, then dip in the egg and coat in the breadcrumbs, shaking off the excess as you go. Set aside on a tray.
Heat 0.5cm oil in a large frying pan until shimmering hot, then add the breaded chicken. Cook for 2-3 minutes on one side until deep golden, then flip and repeat on the other side for the same time. Once the chicken is cooked through (cut into one to check), pile into buns with the rocket and sticky onions. Serve with chilli mayo, if you like.