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1. In a large pot, heat the olive oil over medium heat. Once hot, add the minced garlic and grated ginger. Sauté for about 1-2 minutes until fragrant, being careful not to burn them.
2. Add the sliced shiitake mushrooms to the pot. Cook for about 5-7 minutes, stirring occasionally, until the mushrooms are tender and have released their moisture.
3. Pour in the vegetable broth and bring the mixture to a gentle simmer. Allow it to simmer for about 10 minutes to let the flavors meld together.
4. After simmering, stir in the white miso paste and soy sauce. Mix well until the miso is fully dissolved into the broth.
5. Next, add the coconut milk to the pot. Stir to combine and let the broth simmer for an additional 5 minutes.
6. While the broth is simmering, bring a separate pot of water to a boil. Once boiling, add the udon noodles.
7. Cook the udon noodles according to the package instructions, usually about 3-5 minutes, until they are tender but still chewy.
8. Once cooked, drain the noodles and rinse them under cold water to stop the cooking process. Set aside.
9. After the broth has simmered with the coconut milk, add the chopped bok choy and julienned carrot to the pot. Stir well and let the vegetables cook for about 3-4 minutes until they are tender but still vibrant in color.
10. Check the seasoning of the broth. If needed, adjust with more soy sauce or miso paste according to your taste preference.
11. To serve, place a portion of the cooked udon noodles into each bowl.
12. Carefully ladle the hot miso broth with vegetables over the noodles, ensuring each bowl gets a good mix of mushrooms, bok choy, and carrots.
13. Garnish each bowl with chopped green onions, a sprinkle of sesame seeds, and fresh cilantro if desired.

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