Preheat the oven to 200C/400F/Gas 6.
Score the cut surface of the onion multiple times with a sharp knife and drizzle with one tablespoon of the olive oil.
Lay the onion halves cut-side-down in a small, ovenproof, non-stick frying pan and fry for four minutes, or until golden brown.
Turn the onion halves up the other way in the pan and transfer to the oven to roast for 8-10 minutes or until soft in the centre.
With the remaining one tablespoon olive oil, fry the sausage for 2-3 minutes until golden-brown on all sides.
Remove the sausage from the pan and slice in half lengthways.
Fill the centre of the sausage with the cheddar slices and place in the oven alongside the onion. Bake for six minutes or until the sausage is cooked through. Place on a serving plate and serve hot.