A spicy, bright ginger broth with tender carrot noodles and wilted spinach is a light, vegetarian soup that satisfies.
Place fennel seeds in a small, dry skillet. Set skillet over medium heat. Toast seeds, shaking skillet occasionally, until aromatic, 2 to 4 minutes. Transfer fennel seeds to a medium saucepan; set pan and seeds aside.
Repeat toasting process with the sesame seeds, toasting in the dry skillet until aromatic, 1 to 3 minutes. Transfer the sesame seeds to a small bowl, and set aside.
Add the ginger, cardamom, and star anise to the saucepan containing the toasted fennel seeds. Add 8 cups water, and cover. Set over high heat, and bring to a boil. Reduce heat; simmer, with lid ajar, until liquid has reduced to about 4 cups, 45 to 60 minutes.
Using a vegetable peeler, make the carrot noodles: Run the peeler along the length of each carrot, and rotate the carrot a quarter-turn with each new strip. (Alternatively, use a turning slicer)
Strain the ginger broth through a fine sieve set over a heat-proof bowl; discard solids. Return broth to saucepan; set over medium heat. Add carrot noodles. Cook until noodles are just tender, about 3 minutes.
Add the spinach, and cook until just wilted, about 30 seconds. Season broth with salt and pepper. Using a slotted spoon, divide the carrots and spinach among four soup plates. Divide the broth among the plates. Top each serving with the reserved toasted sesame seeds and the scallions.