Peel and cut the potatoes into 2 cm cubes. Wash under running cold water to remove some of the starch. Dry the potato pieces off.
Place in a saucepan with cold water and bring to the boil. You want to cook them until the edges of the cubes start to 'feather', around 10 minutes.
Drain and place on a cooling rack and place in the freezer for around an hour.
Heat a neutral oil in a deep saucepan to 130°C. Carefully add the potato cubes and cook until they start to take colour. At this stage increase the heat to 180°C until the potato cubes are a light golden brown. Remove and place on a cooling rack lined with kitchen paper. Keep warm until ready to use.
Fry the Mexican chorizo on low for a few minutes to warm it up, then transfer to the oven to keep warm.
To make extra chilli oil, leave a few pieces of chorizo in the pan and add some more oil until the oil takes on some of the colour of the chorizo.
Slice the purple shallots and long chillies, wash the fresh coriander (cilantro) and remove leaves from the stems, quarter and de-seed the lime, and break up the white cheese into small crumbly pieces.
Heat the soft flour or corn tortillas over a dry skillet then transfer them to your serving plates and cover with a clean cotton tea towel to keep them warm.
Fry the eggs individually in a small saucepan with a little oil until almost set. We love a runny yolk, but cook to your preference.
Assemble your tacos: place the fried eggs on one side of the tortilla then the potato and chorizo; sprinkle the purple shallots, crumbly cheese, chilli slices, and coriander leaves on top; and douse with the spicy chorizo oil.
Serve immediately with additional lime quarters, garnishes and hot sauces.