Begin by preparing all the ingredients. Remove the skin from the chorizo and slice it into 5 mm rounds. The onion needs to be peeled, sliced in half and then each half sliced fairly thickly into half-moon shapes.
Remove the stalk from the pepper and then halve it, scooping out the seeds. Slice it first into quarters and then each quarter into slices. The tomatoes need to be skinned, (see our Video Techniques) so place a nick in the bottom of the tomato, pour boiling water over them, leave for 30 seconds, immediately transfer them to cold water, drain them and slip off their skins.
Slice each tomato in half, squeeze each half gently to remove the seeds, then chop the flesh into small cubes. Peel and finely chop the garlic.
Next take the frying pan, place it over a high heat and add the olive oil. When the oil is really hot, brown the chorizo pieces, tossing and turning them around until they turn slightly brown at the edges.
Using a draining spoon, transfer the chorizo from the pan to a plate. Next add the onion and pepper to the pan and toss these around, keeping the heat high, until they're nicely tinged brown at the edges and softened, which will take about 4 minutes.
Pre-heat the grill.
Now add the garlic and the chilli stir it around then add the tomatoes and return the chorizo to join the rest of the ingredients and add the olives. Finally, give everything a good mix and season with salt and freshly milled black pepper.
Then if you are using a gratin dish transfer the hot pepper mixture into the dish. Make 4 indentations with the back of a tablespoon in the pepper mixture and carefully slip an egg into each one (or you can break them into little bowls first then slip them in).
Season the eggs with some salt then sprinkle them with the slivered cheese and a little paprika. Place the frying pan or dish on the top shelf of the grill about 10 – 13 cm from the heat to grill for 4 - 5 minutes (or a little longer, depending on how you like your eggs).
I think this needs some quite robust red wine and some warm crusty baguette served alongside.