Peel the onion, then cut in half and finely chop. Cut the top and bottom off the green pepper, then remove the core and cut into dice. Cut the red chillies into slices, if using.
Heat the oil in a large non-stick frying pan over a medium heat. Add the mince and sauté for 4-5 minutes until well browned, breaking up any lumps with a wooden spoon.
Add the onion to the mince with the green pepper and half of the chillies, if using and sauté for 5 minutes. Stir in the tomato puree, honey, vinegar, Worcestershire sauce and kidney beans. Season and simmer for 15 minutes until thickened, stirring occasionally.
Preheat the grill to medium. Split the rolls and lightly toast. Trim the lettuce, then shred and put on the bottom of each bun. Spoon the beef mixture on top. Scatter over the Cheddar with the rest of the chillies, if using, then sandwich together with the tops of the buns and arrange on plates to serve.