Peel the potato and grate it in a bowl with the thick side of the grater. Put it inside a towel and squeeze it well to remove the liquids.
Transfer the grated potato into a bowl and add the thyme, the salt, the pepper, the rosemary, the chopped garlic and mix well.
Place a 22 cm frying pan on low heat and add the olive oil.
Add the potato and spread it with a spoon in order to cover the whole surface of the pan. We braise each side for 10 minutes. Remove to a plate and leave aside.
Put the same pan on the stove and add the bacon. Roast each side for 1 minute and remove.
Wipe the pan and put it on moderate heat.
Add the butter, let it melt and break the eggs. Add salt, pepper and leave 2 minutes to cook.
Put it on the plate with the potato and the bacon and serve with arugula, cherry tomatoes and grated feta cheese.