Heat the vegetable oil in a large pot or Dutch oven over medium heat.
Add the sliced shiitake mushrooms and cook for 5 to 8 minutes, stirring occasionally, until softened and lightly browned at the edges.
Add the tamari, vegetable broth, grated garlic, grated ginger, julienned carrot, frozen dumplings, and half of the sliced scallions, then stir gently to combine.
Bring the broth to a boil, then reduce the heat to a gentle simmer and cook for about 4 minutes, or until the dumplings are heated through.
Remove the pot from the heat and add the spinach, rice vinegar, and lime juice.
Stir gently for 30 to 60 seconds, until the spinach wilts, then taste and adjust the seasoning as needed.
Ladle the soup carefully into bowls and garnish with the remaining scallions and sesame seeds.
Serve with extra tamari and Sichuan chili crisp on the side, if desired.