Make pasta using well method.
Bring 3 quarts of water to a boil and add 1 tablespoon of salt. Set up an ice bath nearby. Blanch the wild spinach in boiling water for about 2 minutes, then remove and immediately refresh in the ice bath. Once cooled, coarsely chop then dry thoroughly using paper towels.
Boil the potatoes until they are soft (about 45 minutes), then pass through a ricer.
Combine the spinach, potatoes, onion, and cheese. Set aside.
Using a pasta machine, roll out the dough on the thinnest setting. Cut the sheets into 4- to 5-inch squares. Place 1 tablespoon of the filling in the center of each square, bring two opposite corners together to form a triangle, and press the edges together firmly to seal. (At this point you may freeze the ciaroncie on cookie sheets between layers of wax paper or parchment.)
In a 12-inch to 14-inch sauté pan, heat butter until foam subsides. Add poppy seeds and turn heat to low.
Meanwhile, drop the ciaroncie in the boiling water and cook for 2 minutes or until they float to the surface. Using a slotted spoon, drain the ravioli and add them to the sauté pan.
Add chopped parsley to the pan. Toss gently for 1 minute over medium heat to coat. Plate the ciaroncie carefully with a spoon. Spoon extra sauce over each serving, top with the remaining parsley, and serve immediately.