Add the sweet onion, carrots, and ginger to the pot. Sear them until their edges begin to brown.
Add the chicken broth and bring the mixture to a boil. Reduce the heat, cover the pot, and let it simmer for 1 hour.
Strain the broth through a fine-mesh sieve to remove the vegetables. Discard the solids and add salt to taste.
Divide the hot, clear broth among four bowls and top each with sliced scallions and mushrooms.