Squeeze the avocado flesh into a blender, discarding the stone and skin. Squeeze in all the juice from 2 limes, rip in the coriander stalks, add the yoghurt and a splash of oil and whiz until smooth, then season to perfection.
Peel the onion and carrot. Ideally in a food processor, or using a box grater and good knife skills, grate the onion and carrot, then finely slice the cabbage. Very finely slice the chilli by hand, then tip everything into a large bowl. Add most of the coriander leaves, then pour over the avocado dressing and toss together well. Taste and season to perfection again, if needed. Whisk all the eggs together in a bowl, with a splash of water to loosen and a pinch of salt and pepper.
Put a large non-stick frying pan on a medium-low heat. Once fairly hot, put in a tiny drizzle of oil followed by a quarter of the egg mixture. Swirl it all around the pan, grate over a quarter of the cheese and let it melt, then cook the omelette gently without colouring it, so it's soft, silky and smooth, for just under 2 minutes, only cooking on one side. Slide it on to a plate, spoon over a quarter of the avocado slaw, then gently fold up the sides and roll over. Serve with a wedge of lime and a few extra coriander leaves. Repeat with the remaining ingredients, serving them up as you go.