Combine chicken broth, mushroom caps, ginger, scallions, soy sauce, and sesame oil (optional) in a large, shallow sauté pan. Bring to a boil over high heat, then lower heat and simmer for 2–3 minutes.
Add salmon fillets, and cover with a tight-fitting lid. Cook gently over low heat for 4–5 minutes or until the salmon flakes easily with a fork in the thickest part (to a minimum internal temperature of 145 °F).