Peel the potatoes and cut off a bit from each to make them flat-bottomed. Pour water over them in a pot and boil for a bit, just enough for them to soften slightly, but do not mash them – leave them half boiled. The goal is to be able to carve them out with a spoon.
Cut the bacon and onion into small pieces. Grate the cheese and carrot. Carefully remove the stems of the mushrooms and chop them finely. Combine everything (excluding the potatoes) in a bowl and mix in the eggs. If you want, you can blend (before mixing with the eggs).
Carve out the potatoes with a suitable spoon and fill them with the mixture. Cap their tops with the mushrooms caps.
Arrange the potatoes in a buttered baking dish and pour in 1 finger width of salted water. Add 2 tablespoons of oil and put them in a moderate oven for 30 minutes. It is best to cover them in the last 10 or so minutes.