Heat the oil in a large soup pot over medium-high heat. Add the shallots and cook, stirring regularly, for 5–7 minutes or until they char around the edges.
Cook the carrots:
Add the carrots and cook in the oil for an additional 5 minutes. Season all over with salt and pepper.
Add the lemongrass and garlic. Stir to coat and cook for 1 minute until fragrant.
Simmer the broth:
Pour in 4 cups of water. Bring to a boil and then reduce heat to medium. Rapid simmer for 30 minutes or until the carrots are fork-tender and the liquid has reduced by half. Season to taste with salt and pepper. Turn off the heat.
Blend the carrots:
Using an immersion blender, blend the carrots until completely smooth. You should have about 2 cups of purée.
Finish the soup:
Return the heat on the carrot purée to low. Stir in the coconut milk and add 1–2 cups water, depending on how thin you want the broth to be. Stir in 1 teaspoon chili oil and 1 teaspoon sesame oil. Taste and season once more. Simmer for 5 minutes.
Cook the noodles:
Bring a large pot of salted water to a boil. Cook the noodles according to the package instructions. Drain, rinse, and divide between bowls.
To serve:
Ladle the carrot broth on top of the noodles. Garnish with Thai basil, jalapeño, microgreens, and a sprinkle of sesame seeds. Enjoy!