Bring a medium pot of water to a boil over high heat. Add the spinach and cook for 30 seconds, until it turns a vivid green, then, using a slotted spoon, transfer it to a bowl of ice water.
Chill thoroughly and drain. Wrap the spinach in a clean cheesecloth or tea towel to wring out excess moisture, then roughly chop it and set it aside.
In a small bowl, whisk together the eggs, milk, and 1/4 teaspoon of the salt and set aside.
In a medium nonstick skillet, heat the vegetable oil over medium-low heat until a few drops of water added to the pan sizzle and evaporate. Pour in the egg mixture and cook, stirring occasionally, for 4 minutes, just until the eggs form fluffy curds but have not fully set; they should still be slightly runny. Remove from the heat and let cool in a medium bowl.
Use your hands to gently fold the eggs, sesame oil, oyster sauce, remaining 1 1/4 teaspoons of salt, and pepper together until fully combined. Gently fold in the spinach and mix until fully incorporated.
Dust your work surface with a little more flour, then knead the dough as before. Work out all those lumps; after kneading about ten times you should have a satin-smooth dough that forms a clean ball you can easily push into, like the gel of a shoe insert.
Form your dough into a log, dust a dough scraper with a little flour, and cut the dough into four sections.
Roll each section into a log and chop it into six pieces for a total of twenty-four balls of dough, each about an inch in diameter. Toss the balls with a light coating of flour and cover with a lightly moistened towel.
Gently smash the balls of dough into flat disks, then lightly roll an Asian-style rolling pin across them to flatten them out a bit more.
Hold one disk by its edge and firmly but gently roll your pin from the disk's edge to its center. Roll the same edge a few more times, using more pressure at the edge than at the center. Use your other hand to turn the dough disk and reveal a new edge of the disk; roll again. Continue until all edges are rolled out and the wrapper is about 3 to 4 inches in diameter.
Hold your rolled-out wrapper up to a light. If you can see through it faitly, your wrapper is ready to go. Otherwise, keep rolling. Roll the edges to half the thickness of the center of the wrappers.
Bring a large pot of water to a boil.
Holding a wrapper in your palm, use a fork to add about 1 tablespoon of the filling to the center of the wrapper, then lightly pat down the filling with the fork to get rid of any air bubbles.
Fold the dumpling into the round yuan bao shape- Once the filling is in place, cradle the wrapper in one hand, fold the edge closest to you over the filling, and pinch the dumpling shut.
Now seal it for good: cradle the dumpling in your palms, clasing the sealed edge between your thumbs and index fingers, and squeeze it shut while pushing inward, making sure to squeeze out any air bubbles. The dumpling's belly should form a teardrop shape between your thumbs, which will create the round yuan bao shape.
Inspect the dumplings for any fissures that could rupture during cooking and pinch them shut, leaving as little open space as possible between the filling and the sealed edge of the wrapper. Repeat with the rest of the wrappers.
Working in batches, add the dumplings to the pot, 6 at a time. Boil for 2 minutes on high, then reduce the heat to medium-high and cook for 1 minute, then reduce the heat again to medium and cook for 2 more minutes. The dumplings are ready a minute or so after they rise to the surface; their skins will turn puffy.
Using a slotted spoon, gently transfer the dumplings to a plate and serve immediately. Bring the water back to a boil over high heat and repeat with the remaining dumplings.