First, make the caramelised onions. Heat a large frying pan on a medium-high heat and add the olive oil. Once hot, tip in the onions. Turn the heat to low and fry the onions for 40 minutes, stirring every few minutes
After 40 minutes add in the balsamic vinegar and sugar and continue cooking for 20 minutes. Set aside
Split the vegan mince into four 60g/2.25oz balls and flatten into circles around 7mm/0.25 inch thick
Heat the vegetable oil in a large frying pan over a medium-high heat until very hot. Fry the patties until brown and crispy. Flip and top each patty with a slice of cheese. Cover with a lid until the cheese has melted. You can add a teaspoon of water to help create steam and melt the cheese. Once the cheese has melted remove the lid and cook until the patty is crisp and brown.
Whilst the patties are cooking split the buns in half. Place the buns under a hot grill, split sides facing up, until lightly toasted.
Spread the bottom bun with mayo, top with shredded lettuce, a patty, caramelised onion, another patty, ketchup, and the top bun. Serve hot with fries.