Heat a tablespoon of olive oil in a medium-sized stockpot over medium heat. When the oil is shimmering, toss in the diced shallots. Sauté them for about 4-5 minutes, stirring occasionally, until they become translucent and begin to soften. This softening process releases their mellow sweetness and creates a solid flavor base.

While those shallots are cooking, chop the white part of the green onions finely. Set aside the green tops for later use as a garnish. Once the shallots are ready, stir in the minced garlic and ginger, along with the chopped white green onions. Keep stirring for another 1-2 minutes. The fragrance of garlic and ginger will fill your kitchen; trust me, it’s heavenly!

Carefully pour in the low-sodium chicken or vegetable broth and increase the heat to bring it to a gentle simmer. Add the star anise and soy sauce, stirring to combine. Cover the pot and let it simmer for about 10 minutes. This allows the flavors to meld beautifully.

After 10 minutes, take off the lid and fish out those star anise pods. Their job is done! Now, it's time to add the sliced mushrooms, uncooked noodles, chopped bok choy, and thinly sliced carrots. Reduce the heat and let everything simmer for an additional 5-8 minutes, or until the noodles and bok choy are tender. The vibrant colors of the veggies should be shining through!

Once the soup is cooked, take a moment to taste and adjust the seasoning. You may want to add a bit more soy sauce or a pinch of salt. Then, portion the soup into bowls. Garnish each bowl with sesame seeds, the green parts of the green onions, and a sprinkle of red pepper flakes if you like a bit of heat.