In a large deep pan or Dutch oven, heat the olive oil on medium heat and caramelize the leeks until they’re a light golden brown. This will add so much flavor to the broth. If you don’t cook with oil you can caramelize them in a little bit of broth.
Add the carrots, mushrooms, garlic, vegetable broth, water, tamari, star anise, ginger, bay leaves, and the cinnamon stick and bring to a boil. Once the broth is boiling, reduce the heat to a simmer and let it cook for 30 minutes.
While the broth is simmering cook the rice noodles according to the instructions on the package.
Add the chopped cilantro and squeeze the lime juice into the soup and stir it to combine. Salt to taste.
Divide the noodles into four bowls and pour the broth and mushrooms over the noodles. Garnish it with more cilantro and basil leaves.