Place your pan on the Q barbecue and preheat for 10 minutes.
Add the oil, onion, garlic, and chorizo sausage, close the lid, and cook for 6 to 7 minutes, stirring once or twice. Add the sugar, paprika, chilli, and baked beans. Stir in well, close the lid, and cook for 4 to 5 minutes.
With the back of a spoon, make four indentations in the top of the mixture and crack an egg into each. Sprinkle the cheese over the top of the mixture and season with salt and pepper to taste. Close the lid and cook for a further 6 to 8 minutes.
Remove the pan from the barbecue and sprinkle the chopped parsley over the top.