Start by preparing the cups for steaming the dumplings. Grease each cup with a knob of butter or other solid fat, then dust lightly with flour, shaking out any excess.
Cut 2 cups white bread into small cubes, about ¾ inch thick. Heat ⅓ stick unsalted butter in a frying pan and fry the cubes until golden brown, stirring to ensure even frying. Once done, remove from heat.
Rinse ½ cup green parsley leaves, drain, and chop them coarsely, using only the leaves and setting the stems aside. Sprinkle the chopped parsley over the fried bread cubes.
Separate 1 egg yolk from the white, placing the white in a clean bowl.
In a mixing bowl, whisk together 1 ¼ cup milk, 1 cup all-purpose flour, and egg yolk until smooth, using a hand whisk to prevent lumps.
In another bowl, beat the egg white with ½ teaspoon salt until stiff peaks form.
Gently fold the beaten egg whites and fried bread cubes into the milk mixture. Fill each prepared cup with the batter, leaving about an inch (2 cm) of space at the top.
Bring about two inches (5 cm) of water to a boil in a large pot. Place the filled cups in the pot, cover with a lid, then reduce the heat to low. Steam the dumplings for 30 minutes.
Carefully remove the cups from the pot. I used a pair of tongs. Let the dumplings cool for about five minutes, then loosen them from the cup edges with a thin knife and tip them out. Slice into ½-inch (1.2 cm) pieces and serve.