Step 1
Pour boiling water over shiitake mushrooms and let sit until soft enough to slice about 1 hour.
Step 2
Meanwhile combine chestnuts and tofu in a large bowl. Add ground pork green onions garlic and ginger. Pour in rice wine soy sauce salt cayenne brown sugar and egg. Dust with cornstarch. Mix with a clean hand until thoroughly combined. Cover with plastic wrap and refrigerate for at least 1 hour.
Step 3
Form mixture into 6 large meatballs with wet hands.
Step 4
Set an oven rack about 8 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil and oil lightly. Place meatballs on the prepared baking sheet.
Step 5
Broil in the preheated oven until browned 8 to 10 minutes. Remove from the oven and let cool while prepping the pot.
Step 6
Trim off the bottom of the head of cabbage and slice 1/2 of the head. Arrange sliced cabbage on the bottom of a large soup pot or Dutch oven. Arrange the remaining leaves on the top. Slice and scatter the mushrooms on top of the cabbage; reserve shiitake liquid. Nestle the meatballs into the cabbage leaves and pour juices over.
Step 7
Strain reserved shiitake liquid into a bowl. Add chicken broth soy sauce sherry sesame oil brown sugar and cornstarch. Whisk until dissolved. Add to the pot pouring over each meatball. Bring to a boil over high heat.
Step 8
Reduce heat to medium-low cover and cook for 20 minutes. Uncover and raise heat to medium-high. Continue cooking basting the meatballs often until liquid reduces slightly and meatballs are no longer pink in the centers about 10 minutes. Taste for seasoning.
Step 9
Ladle into serving bowls and arrange cabbage over the meatballs. Top with green onions and chili oil.