Wash the potatoes, and cut them into 2cm chunks (you can peel them first if you prefer; I didn't bother). Boil them in a large pan of water for around 10 minutes, or until soft.
Meanwhile, heat the oil in a large frying pan and add the onion and garlic. Cook over a medium-low heat for around 10 minutes, stirring regularly, until very soft.
When the potatoes are soft, drain them and mash thoroughly. Add the cooked onions, grated cheese, and plenty of salt and pepper, and mix well until the cheese has melted. If you have time, allow to cool for half an hour (it makes the mash easier to shape, but don't worry if you don't have time).
To prepare for breading, place the flour in a wide bowl or deep plate, and do the same with the breadcrumbs in a separate dish. Lightly beat the eggs in a wide bowl.
Using your hands, shape around an eighth of the potato mixture into a patty, and coat it in the flour. Next, coat it in the beaten egg, shaking off any excess, then cover it in breadcrumbs. Place it on a plate or baking tray ready to be fried. Repeat with the remaining potato mixture.
Once you've breaded all of the potato mixture, coat the bottom of a frying pan with oil, and place over a medium heat. When the oil is hot enough that it makes a breadcrumb sizzle, add the first batch of crisp bakes (I fried 3 at a time - don't overcrowd the pan). Cook for a few minutes until the underside is golden brown, then flip and repeat with the other side. Transfer to a lined baking sheet and repeat with the remaining crisp bakes. The crisp bakes may expand a little while baking, so don't leave too much space between them.
When all of the crisp bakes have been fried on both sides, place in the oven and cook at 200°C (Gas Mark 6 / 400°F) for around 30 minutes, until piping hot and crispy.