Heat vegetable oil in a deep heavy-bottomed pan.
Soak onion rings in buttermilk for 30 minutes.
Mix flour, polenta, salt, pepper, and chilli powder on a plate.
Remove onion rings from buttermilk ensuring plenty of liquid clings to them.
Dredge each ring in the flour and polenta mixture.
Fry rings in batches of six for 4 minutes until golden.
Remove with a slotted spoon and drain on kitchen paper.
Season the mince with salt and pepper in a bowl.
Divide the mince and mould into four patty shapes.
Brush patties with olive oil and griddle for 4 minutes per side.
Assemble burgers in charred buns with mayonnaise, lettuce, tomato, and gherkins.
Serve onion rings with salt and a bowl of balsamic vinegar.
Place burgers on plates alongside the onion rings.