Start by making the hash brown. Heat the oil and butter in a small frying pan, then mix together the grated potato and onion. Squeeze any excess liquid out of the potato and onion using your hands. Pat the mixture with kitchen towels, then toss with the salt and pepper. Form into a thin patty and fry in the oil for 5 minutes. Turn over and fry for 5 more minutes until browned, then place in the oven on very low to keep warm.
Butter the bread on both sides using all of the butter.
Heat up a griddle plate and place the bread on the griddle. Cook on one side until the bread is toasted and griddle lines appear. Turn the bread over and sprinkle the cheese on one of the slices. Continue to cook until the bread is toasted on both sides and the cheese is melted (you can place the toast slice with cheese under the grill for a minute if it doesn’t melt enough). Once cooked, put to one side.
Place the bacon on one side of the griddle and cook for 1 minute, then pour the oil onto the other side of the griddle. Allow the oil to heat, then crack the egg on the griddle. Turn the bacon over, and cook until the bacon is crisp and the egg is cooked (but the yolk is still runny) – about 2-3 minutes. Turn off the heat.
Assemble the BLT by placing the toast slice with cheese on the bottom. Top with the sliced tomato, 2 slices of bacon, some ketchup and another slice of toast. Top with the lettuce, hashbrown, the rest of the bacon, the fried egg and the third piece of toasted bread. Season with salt and pepper and serve with more ketchup.