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Preheat the oven to 200C/400F/Gas 6.
To make the beef mixture, place the butter and olive oil in a medium frying pan over a high heat. Add the onions and peppers and fry for two minutes.
Add the beef and paprika and fry for another minute.
Add the red wine and balsamic vinegar, bring to the boil and boil for one minute.
Add the beef stock and the cream, bring to the boil and reduce the heat to simmer for ten minutes, until the sauce has thickened.
To make the cheesy polenta, place the vegetable stock in a medium saucepan over a high heat and bring to the boil
Add the polenta gradually, in a steady stream, stirring continuously. Cook for five minutes.
Add the butter and cheddar and stir until melted and smooth. Season, to taste, with salt and freshly ground black pepper.
To serve, place the polenta onto a serving plate, leaving a space in the middle. Pour the beef stroganoff mixture into the middle and garnish with the chopped chives.
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