In a large saucepan, braiser, or Dutch oven, over medium heat, heat 3 tablespoons of neutral-tasting oil, like grapeseed or vegetable oil. Add your sliced shiitake mushrooms and grated or minced ginger. Cook until just fragrant, about 1-2 minutes.
Add in the soy sauce, bamboo shoots chicken broth, and white pepper. Stir to combine and bring to a boil.
When the mixture comes up to a boil, reduce the heat to maintain a low simmer and add in the frozen dumplings. Keep it at a low simmer for about 5-7 minutes, stirring occasionally, until the dumplings are cooked through.
In a small bowl, whisk together 1/4 cup water and 2 tablespoons cornstarch to make a slurry. When the dumplings are cooked through, pour the slurry into the soup and stir. Add the white vinegar and stir to combine. Stir and cook for about 2 minutes, until the broth has thickened.
Turn off the heat and taste for seasoning. If it needs more vinegar, add another tablespoon of vinegar and stir to combine. Add kosher salt and black pepper if needed.
Ladle the soup into bowls and garnish with as many hot pepper slices as you like, top it off with cilantro or sliced scallions.