Heat oil in a large saucepan over medium heat.dd apple, fennel and onion. Cook, stirring frequently, until softened, 6 to 8 minutes.
Stir in thyme, sage and nutmeg. Cook, stirring, until fragrant, about 30 seconds.
Pour in broth and vermouth (or wine), stirring to scrape up any browned bits. Bring to a simmer.dd mussels and stir to combine. Return to a simmer. Cover, reduce heat and simmer until the mussels open, 6 to 8 minutes. Stir; discard any unopened mussels before serving.