Mix the pumpkin dough: In a large bowl, combine flour, pumpkin puree, salt, and warm water a little at a time. Stir until a shaggy dough forms, then knead on a floured surface for about 5 minutes until smooth.
Rest the dough: Cover the dough with a damp towel or plastic wrap and let it rest for 30 minutes. This relaxes the gluten so the wrappers roll out easily without snapping back.
Mix the filling: In a separate bowl, combine ground chicken, shredded cabbage, scallions, ginger, garlic, soy sauce, sesame oil, and egg. Stir well until the mixture feels tacky and holds together when pressed.
Divide and roll wrappers: Divide the rested dough into 16 equal pieces and roll each into a thin round about 3 inches wide. Keep the rounds covered as you work to prevent drying out.
Fill each wrapper: Spoon about 1 tablespoon of the chicken filling into the center of each dough round. Avoid overfilling, since that makes sealing harder and can cause bursting during steaming.
Seal into a ball: Gather the edges of the dough up and over the filling, pinching and twisting at the top to seal completely. Roll gently between your palms to smooth it into a round ball shape.
Press pumpkin ridges: Press a piece of kitchen twine or the dull edge of a knife into the sides of each ball to create 6 to 8 evenly spaced grooves, mimicking pumpkin ridges. Press firmly enough that the lines stay visible.
Add the stem: Insert a 1-inch piece of chive into the top of each dumpling where the dough was sealed, pressing gently so it stands upright like a pumpkin stem.
Steam the dumplings: Arrange the dumplings in a lined steamer basket, leaving space between each one. Steam over simmering water for about 10 minutes, until the dough turns slightly translucent and feels firm when pressed.
Make the dipping sauce: While the dumplings steam, whisk together soy sauce, rice vinegar, sesame oil, and chili flakes in a small bowl. Taste and adjust the chili flakes for your preferred heat level.
Serve warm: Transfer the dumplings to a platter once the ridges and stems are set from steaming, and serve them with the dipping sauce alongside.