Boil the potatoes until they become fork tender (about 20-30 minutes, depending on the size).
Drain, peel, and mash the potatoes with a potato ricer, then add the flour while they are still warm (overwise they will become sticky). Mix well until you get a nice soft non-sticky dough.
Cut the dough in smaller parts and roll them with your palms to get a long roll about 1 inch (2cm) thick. Keep the surface and the dough smooth with flour to prevent stickiness.
Now with a dough-cutter cut the gnocchi about 2-3 cm long. You can then roll them on a fork or on a gnocchi board to get the typical gnocchi lines. Let them rest on a clean towel until you’re ready to cook them.
Make the 4 Cheese sauce
In a saucepan melt the butter and mix in the flour to make a roux. Cook for a minute or two, then add the room temperature milk or cream. Mix with a wooden spoon until the roux is completely melted.
Turn down the heat and add all the grated cheeses. Let the cheese melt and stir occasionally to make sure they don't stick to the pan.
Add black pepper and season to taste. If the sauce is too thick, add some more milk. Stir thoroughly until you have a smooth cream.
In a large pot bring to boil salted water and toss the gnocchi one by one so they will not stick. It will take 1-2 minutes to cook.
As soon as the gnocchi float to the surface, it means they are ready! Take them out with a skimmer and add them directly in the pot with the cheese sauce.
Serve immediately.
Video
Notes
What is the best way to reheat leftover gnocchi? You can store leftovers in an airtight container in the fridge for up to 2 days and you can reheat leftovers either in the microwave or on the stove, but I suggest you add a few tablespoons of milk to the sauce to make it smooth and creamy again.