Combine meat, mushrooms, green onion, soy sauce, sesame oil, rice vinegar, ginger, salt, and pepper in a bowl. Mix well using your hands until all ingredients are well-combined.
Fill a small bowl with cold water. Working with 1 dumpling at a time, dip every side of the wrapper in the water, about ½" into the wrapper.
Add 1 ½ teaspoon of filling to middle of wrapper. Fold opposite corners of the wrapper together, then fold the smaller edges together towards the middle until the filling is completely enclosed.
Snip off the top pieces of the dumpling and discard. This step is optional but if you don't remove the loose corners, they can get tough during cooking.
Place finished dumplings on parchment paper-lined sheet pan. Cover and refrigerate for up to 4 hours before cooking.
Soup:
Heat 2 tablespoon canola oil in large pot over medium-high heat. Add in shallots and ginger. Cook for 2-3 minutes or until fragrant and starting to soften, stirring frequently.
Add in shredded cabbage. Cook, stirring frequently, for 3-4 minutes or until cabbage is starting to soften. Add in soy sauce, stir to coat, and cook for an additional 1 minute.
Add in broth and bring to a boil. Simmer for 15-20 minutes.
Cooking Dumplings:
Heat 2 tablespoon oil in electric skillet on medium-high heat or in large skillet. If using a skillet, you may need to work in batches.
Swirl pan to completely coat with oil. Place dumplings in a single layer into electric skillet, bottom side down. You can dip the dumplings in the oil and move them around to make sure the all the bottoms have oil on them.
Cook for 3-5 minutes or until bottoms of dumplings are golden brown. Add in 2-3 cups of hot broth (or enough broth to go about halfway up the dumplings in the pan). Cover and cook an additional 3-5 minutes.
Remove lid and cook until broth is mostly evaporated.
Arrange dumplings in bowls (about 8 per serving) and divide broth/vegetables among bowls. Top each bowl with 1 tablespoon green onions and a pinch of red pepper flakes (optional).
Ramen Broth:
There are a few options for broth for this recipe:
If you have some ramen broth frozen from a previous recipe, you can use that. Recipes for ramen broth:Whitetail RamenPork Belly Ramen
You can buy store-bought ramen broth or concentrate.
You can boil low sodium broth/stock with green onions, garlic, ginger, mushroom stems, bonito flakes, soy sauce, fish sauce, etc. for 20-30 minutes to add some extra flavor to the broth. Strain and follow the recipe as normal.