This recipe takes some time, but you can freeze the wontons for up to a month. At the supermarket, you can usually find wonton wrappers next to the tofu.
Finely chop all of the white part and enough of the green part from 1 scallion to measure 1 tbsp. Transfer to a medium bowl. Thinly slice the remaining green part; reserve for garnish. Cut the remaining scallion into 3-inch lengths; lightly smash with the flat side of a large knife.
In the bowl with the chopped scallion, add the pork, 1/2 tsp. cornstarch, 1/2 tsp. sesame oil, the grated ginger (if using), 1/8 tsp. sugar, 1/4 tsp. sea salt, and the pepper. Using a fork, stir vigorously to blend well. Cover with plastic wrap. Let stand for about 15 minutes for the flavors to infuse. If you aren’t using the filling right away, cover and refrigerate for up to 1 day.
Line a baking sheet with parchment paper; dust with cornstarch. On a work surface, arrange 4 to 6 wonton wrappers; using a pastry brush or your finger, paint the edges with water. Using a spoon, scoop out 1 tsp. of the filling. Using another spoon, transfer the filling to the wrapper and place slightly off-center. Fold 1 corner of the wrapper over the filling to the opposite corner to create a triangle. Using your fingers, press from the edge of the filling out to the edges of the wrapper to eliminate any air pockets. Press the edges to seal. (You can stop here or fancy it up by bringing the opposite corners together: Brush the corners with a bit of water. Fold the corners toward the center, overlapping slightly; press to seal.) Place the wonton on the baking sheet. Repeat with the remaining filling and wrappers; space the wontons apart on the baking sheet.
Loosely cover the wontons with a kitchen towel (not terry cloth) or plastic wrap and keep at room temperature. If you aren’t using the wontons right away, cover and refrigerate for up to 3 hours. (Or freeze on the baking sheet until hard, about 1 hour. Transfer to an airtight container. Freeze for up to 1 month. Partially thaw the wontons before boiling.)
Fill a large pot halfway with water. Bring to a boil. Using the flat side of a large knife, lightly smash the sliced ginger. In a large saucepan with a lid, bring the stock, smashed scallion, and smashed ginger to a boil over high heat. Reduce heat to a gentle simmer. Cook until the ginger has lightly infused the stock, 10 to 15 minutes. Discard the ginger and scallion. Partially cover the broth and adjust heat to maintain a gentle simmer.
Add the wontons 1 at a time to the boiling water, using a wooden spoon to nudge them apart and prevent them from sticking together. Adjust heat to maintain a gentle boil. After the wontons have floated to the surface, let them cook until the wrappers are translucent and the filling is cooked through, about 2 minutes. Using a slotted spoon or spider skimmer, scoop out the wontons; allow any excess water to drip back into the pot. Slide the wontons into the hot broth. Add the vegetables. Increase heat slightly. Let the wontons soak up some of the broth and finish cooking for about 1 minute.
Divide the wontons and vegetables among bowls. Taste the broth and add pinches of sea salt or sugar, if necessary, to create a savory-sweet finish. Ladle the broth over the wontons. Top with a dash of sesame oil and the reserved sliced scallion.
Recipe adapted from Vietnamese Food Any Day, by Andrea Nguyen. © 2019 by Andrea Nguyen. Reprinted with permission from Ten Speed Press.