Wash the spinach very well and then pat it dry with cloth or paper towels to absorb all the water. Chop it into fine pieces and transfer it to a bowl.
Boil the potatoes in their skins in hot water for about 20 minutes or until they are soft when pierced with a fork. Then remove the skins and mash them in a separate bowl.
Add the butter and cottage cheese to the bowl of potatoes and mash to a smooth puree.
Mix the spinach with the heavy cream, three-quarters of the mashed potatoes, one cup of the grated Parmesan cheese, the cottage cheese, and the ricotta cheese, and season with salt and pepper.
Beat the 4 eggs and add to the spinach mixture.
Pour the mixture into an oiled round or square baking (9 or 10in) pan with a minimum height of 2.5 inches.
Make a few small wells near the perimeter of the baking pan and insert the remaining mashed potatoes inside, creating a sort of mushroom shape. Then top each mushroom with a bit of butter and grate some Parmesan cheese on top.
Bake in the oven for approximately 25 minutes at 375°F (185°C) until the frittata is set, then increase the temperature to 400°F (200°C) for about five minutes or until the mushrooms are golden brown.
Serve cold, cut into wedges with pickles or a Greek salad.