Heat 2 tablespoons oil in a large saucepan or medium Dutch oven over medium heat.
Add chopped carrots and 2 tablespoons ginger; cook, stirring often, until the carrots begin to soften, 5 to 7 minutes.
Stir in 1½ teaspoons coriander, 1 teaspoon cumin and ½ teaspoon salt; cook, stirring constantly, until fragrant, about 1 minute.
Add trimmed chicken breasts, 6 cups broth and the diced potatoes; bring to a vigorous simmer over high heat.
Reduce heat to maintain a gentle simmer; cover and cook until the potatoes are tender and an instant-read thermometer inserted into the thickest part of the chicken registers 165°F, about 10 minutes.
Transfer the chicken to a plate and let cool slightly, about 5 minutes.
Meanwhile, add 1 package frozen spinach to the soup; simmer, stirring occasionally, until heated through, about 2 minutes.
Stir in 1½ teaspoons tamari.
Thinly slice the chicken against the grain and return it to the soup.
