Heat the oven to 200°C/Fan 180°C/Gas 6. Use a sharp knife to slice the chicken breasts into 1 cm thick strips. Pop in a plastic freezer or sandwich bag. Add 1 tbsp plain flour and a pinch of salt and pepper. Shake well till the chicken is coated.
Beat the egg in a shallow dish. Tip the breadcrumbs onto a plate. Dip each chicken strip first in the egg, then roll in the breadcrumbs to coat them. Pop on a large plate. Cover with cling film and chill in the fridge.
Peel the parsnips and sweet potato. Slice into chunky chips. Bung in a roasting tin. Splash with a little olive oil. Season. Toss the chips together. Roast for 20 mins.
Grease another roasting tin (or baking tray). Spread the breaded chicken strips out on the tray. Roast for 10 mins on the shelf below the sweet potato and parsnip chips.
Rinse and tear a quarter of the cabbage into bite-size pieces. Slice out any thick stalks.
Stir the cabbage into the roast vegetables. Bung back in the oven on the bottom shelf and put the chicken on the top shelf. Bake for another 10 mins till the vegetables and chicken are golden and cooked through.
Spoon the mayonnaise into a serving dish. Serve with the chicken strips and rainbow chips.