If you are starting with fresh potatoes (see tips), cook and mash them and set aside.
Put a little oil in a frying pan, and fry the bacon and the green onion for 5 to 10 minutes. Mix the bacon, onion, egg, parsley and a bit of salt and pepper into the mashed potato. Then fold in the Brie cheese cubes.
Divide the potato mixture into 8, shape into rounds, and roll in some flour.
[You can make these ahead up to here. If you are putting them straight from the refrigerator into the oven, allow a little longer baking time.]
Put about an inch of oil into the frying pan, and get it heating.
When the oil is hot, fry the potato cakes for 3 to 4 minutes on each side.
Put the potato cakes on a baking sheet, and bake in the oven for 15 minutes. Serve hot.
Instead of leftover mashed potato, you can start from scratch with 2 1/4 pounds (or 1.1 kg) of potatoes, about 7 to 8 medium potatoes, that you peel, boil and then mash.