Wash and peel the potatoes. Put in a large pot and boil until soft. Once they are soft, add the butter and milk and then mash the potatoes, then allow it to cool.
Chop the onions and mushrooms and put it in a heated skillet. Make sure you have some butter or oil in the pan first. Cook this mixture until the onions are soft and every thing is golden brown. Once done remove from the heat and put aside.
Once the potatoes are cool add the flour and mix it in, this should make it somewhat dough like. Take a handful and form it into a thin patty. Repeat until all the potatoes are used. (try to make an even amount of patties because you will be combining them)
Take a scoop of onion and mushroom mixture and put it on top of one of the patties. Use about a tablespoon. Take another patty and place it on top of the mixture and press together. Repeat until you use all of the patties.
In a large skillet, take the cooking oil and cover the bottom of the pan. Allow it to heat on medium heat until it sizzle when you put a drop of cool water in it. Once it is hot put in the patties. Cook on each side for about 4-5 minutes, or until golden brown. Remove and place on paper towel to absorb the excess oil.