In a large bowl, combine the ricotta, chard, Parmesan, 2 Tbs. salt, the nutmeg, eggs, and yolks with a large rubber spatula. Mix as thoroughly as possible before adding the flour: once you add the flour you want to mix it as little as possible or the dumplings will be tough and gluey.
Add the flour 1/4 cup at a time and work it in gently with the rubber spatula. Study the dough as you go: is it very sticky? You don’t want it super dry but you want to be able to roll it later to form the dumplings. Stop adding flour when the dough reaches a rollable texture.
Allow the dough to rest for 30 minutes at room temperature (during which time it will continue to stiffen).
When you’re ready to roll the dumplings, flour a board and your hands. Remove the dough to the board and sprinkle some flour on it. Roll the dough into a long rod, approximately 1/2 inch thick. Cut the rod into 1-inch-long dumplings.
Bring a large pot of water to a boil and season lightly with salt. Drop the dumplings in and cook for 3 to 4 minutes, until they float.
Melt the butter in a medium-size pan and lift the dumplings from the boiling water into the pan to finish, tossing them gently. Serve immediately.