Tips: The dried shiitake mushrooms at American supermarkets are delicate and thin. They rehydrate after soaking in hot water for 15 minutes (very handy), but they lack the deep flavor of the thicker ones sold at Asian markets, which may be simply labeled "Dried Mushroom." If you use dried shiitakes from an Asian market, soak them longer (even overnight). You may also need to slice them thinner or chop them smaller. Gently squeeze rehydrated shiitakes to expel excess moisture, then stem and prep as needed.
Chinkiang is a dark vinegar with a smoky flavor. It is available in many Asian specialty markets. If you can't find it for this recipe, you can substitute 1 1/2 tablespoons balsamic vinegar mixed with 1 1/2 teaspoons cider vinegar.
To make ahead: Make the filling (Step 1; omit ginger) and refrigerate for up to 1 day. Refrigerate filled dumplings on baking sheet (Step 5), covered, for up to 3 hours before continuing with Step 6, or freeze until solid, transfer to a zip-top plastic bag or airtight container and freeze for up to 1 month. Partially thaw the dumplings at room temperature on flour-dusted parchment paper before cooking.
Equipment: Parchment paper