For the onion rings, heat the vegetable oil in a deep, heavy-bottomed pan until a bread crumb sizzles and turns brown when dropped into it. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Place the separated rings of sliced onion into a large bowl with the buttermilk to soak for 30 minutes, stirring occasionally.
Place the flour, polenta, salt, freshly ground black pepper and chilli powder into a clean bowl and mix well. Transfer the mixture to a large plate.
Take individual onion rings from the buttermilk, making sure there's lots of buttermilk clinging to the onion.
Dredge each ring in the flour and polenta mixture and set aside, taking care not to shake off any excess flour and polenta coating.
Carefully add the coated rings to the hot oil in batches of six and fry, stirring occasionally, for 3-4 minutes, or until crisp and golden. (The rings may sink to the bottom at first, but will then float to the top as they cook.)
Carefully remove the rings with a slotted spoon and drain on kitchen paper. Repeat the deep-frying process until all of the onion rings are cooked.
For the burger, place the mince into a bowl and season well with salt and freshly ground black pepper.
Divide the mince into four and mould each piece into a patty shape.
Brush each patty with the olive oil and place onto a hot griddle pan. Cook for four minutes on each side, or until completely cooked through.
Place a burger inside each focaccia bun. Spoon over mayonnaise, to taste, and garnish with lettuce, tomato and gherkins.
To serve, place the onion rings into a large bowl and sprinkle with salt. Place a small bowl of balsamic vinegar alongside to dip into.
Place the burgers and buns onto plates and serve with the onion rings.