Heat a pot, with 1 teaspoon of canola oil, over medium-high heat. Add the shiitake mushrooms and cook until they soften and start to turn crispy, about 7 minutes. Remove the mushrooms and set aside.
In the same pot, add another teaspoon of canola oil and add the leeks, garlic, and ginger and cook until softened, about 3 minutes.
Add the kimchi, the kimchi juice, white miso, and soy sauce and cook for about 4 minutes. Add the chicken broth and mushrooms and bring to a simmer. Season with salt and pepper if needed. Allow to simmer for 10 minutes.