Heat oven to 220C/200C fan/gas 7. Toss the chipolatas, bacon lardons and 1 tbsp of the oil together in a large roasting tin. Roast for 20-30 mins until everything is turning brown and crisp – you may want to tip off any liquid and stir it halfway. Use a fish slice to scrape up any stuck bits.
Whisk together the passata, paprika, tomato purée, sugar, brown sauce, 250ml water, a little salt and lots of pepper. Stir into the tin with the beans. Can be made 1 day ahead – cool first, tip into a plastic container, then chill.
Put the tin back in the oven and bake for another 20 mins until thickened and bubbling (add another 10 mins if cooking from chilled).
Turn off the oven but leave the tin in to keep warm while you fry the eggs. Heat the remaining oil in a large frying pan, crack in the eggs and fry them to your liking. Serve the fried eggs with the sausage bake and plenty of hot buttered toast.