Boil Swiss chard leaves in a pot of water for 2 or 3 minutes. Drain, squeeze out excess water and chop with a knife. Pass the ricotta through a food mill and put it in a bowl. Add Parmigiano, egg, chopped Swiss chard leaves and season with salt and nutmeg.
Make a well in the flour, add eggs and water and knead until smooth. Cover with a cotton towel or plastic wrap and set aside to rest for 20 minutes. Roll out dough with a rolling pin or pasta machine to a thickness of less than 1/8 inch.
Cut into 3-inch squares. Place 1 teaspoon of filling in the middle of each square and close in the shape of a rectangle, pressing down on the edges with a fork to seal. Boil in plenty of salted water for 5 minutes, drain and serve with melted butter and Parmigiano.