Peel the carrot and garlic cloves, and remove the roots and green tops from the scallions. Finely dice the carrot, garlic cloves, and scallion whites. Set aside. Reserve the scallions for the garnish.
Mince the quail breasts and fatty pork separately, then combine the meats and mince them again to evenly distribute the pork fat throughout the quail breast.
Place the minced meat and the diced veggies in a medium-sized mixing bowl. Add the sesame oil, fish sauce, soy sauce, and granulated ginger. Mix until well combined.
Prepare a small bowl with 1/2 cup of water near your folding station; this will be the glue for your wontons.
Bring 4 quarts of water to a boil over medium-high heat in a large saucepan (wait on this step if it’s your first time folding wontons, it’ll probably you take a minute to find your rhythm).
Holding an open wrapper in one hand, use your other hand to scoop a small amount (about 2 ounces) of the filling into the wrapper. Dip a finger in the water and wet the top and side edges of the wrapper. Fold the corners together to make a rectangle, taking care to push out all air bubbles and create a good seal. Dab a drop of water onto the top corners of the rectangle and fold them together, creating a “nurse cap” shape. Repeat until all filling has been used.
Now that you’ve finished folding, the water should be boiling. Place a dozen wontons into the boiling water. Turn the heat to high and wait for the water to return to a boil. Once it is boiling again, drop 5 ice cubes into the water to arrest the boil. Repeat this process twice more. Then repeat with the remaining 12 wontons.
Drain the cooked wontons and place them in a mixing bowl. Drizzle 1 tablespoon of chili crisp over the wontons and stir to coat. Place the wontons on a plate and drizzle with the remaining 2 tablespoons of chili crisp. Top with sliced scallion tops for garnish and serve alongside a ramekin of the dumpling sauce for dipping (ponzu, teriyaki, or bachan’s all work here if you can’t find dumpling sauce).