Generously salt a large pan of water and bring to the boil. Add the gluten free pasta and cook as per the pack instructions (usually 10-12 minutes). Meanwhile make the rest of the dish.
Heat the oil in a large, heavy-based pan on a medium-high heat. Once hot, add the beef mince, diced onion, garlic paste and paprika. Continue to fry, while stirring, until the beef has browned, the onions has softened, and any excess liquid from the meat has boiled off - this will take about 5-7 minutes.
Turn the heat down a little (to a medium-low heat) and add the cream cheese and Red Leicester to the beef mixture. Pour over the vegetable stock. Continue to stir the mixture until the cheese has melted and formed a thick and creamy sauce. Leave to simmer gently until the pasta is cooked.
Once the pasta is cooked, add 1-2 tbsp of the pasta water (depending how thick you want the sauce - add more for a thinner sauce) to the beef/cheese mixture. Strain the rest of the water off and then add the drained pasta to the beef/cheese sauce.
Stir the whole dish well, sprinkle over some extra cheese and chopped chives. Serve straight away or place under the grill to melt the cheese - you could even bake in the oven for a further 15 minutes-or-so if you want a crispy cheese topping and more of a cheeseburger pasta bake!