To a food processor, add the garlic, ginger, and half of the scallions to the bowl. Pulse the machine until the veggies are chopped up then add the shrimp and water chestnuts. Run the machine until the shrimp is ground into a paste then turn everything out into a mixing bowl. Add the pork, egg, shredded cabbage, carrots, sherry, chili paste, 2 tablespoons sesame oil, 2 tablespoons soy sauce, lime zest and juice. Combine the ingredients with your hands until evenly mixed.
Give your hands a wash and lay out cabbage leaves on the counter. Divide the meat and veggie mixture among the leaves. Roll them up -- starting at the leafy end and rolling towards the stem end -- just like you'd roll up a burrito, tucking the sides in as you go. Secure it closed with a toothpick, if necessary.
Once all of your cabbage rolls are assembled, place a medium-size pot with a lid over medium-high heat with 2 turns of the pan of vegetable oil, about 2 tablespoons. Add the rice to the pan and cook it for a minute, then add the chicken stock. Bring the liquids up to a bubble, then put the lid on the pot, reduce the heat and cook until the rice has absorbed all of the liquid, 18-20 minutes. Fluff the cooked rice with a fork and stir in all but a small handful of the remaining scallions.
With your rice working, place a large, lidded skillet over medium-high heat with enough chicken stock to fill it by about an inch and bring it to a bubble. Place the cabbage rolls into the boiling stock and put the lid on the pan. Steam the wrappers until the meat has cooked through, about 10 minutes.
While everything cooks, in a small serving bowl stir together the remaining soy sauce, sesame oil and scallions with the honey, ginger slices and a splash of water. Put this dipping sauce onto a serving platter along with the duck sauce and mustard. Serve the Napa rolls on the platter with the scallion rice on the side.