Step 1

Heat 3 Tbsp. oil in a large saucepan over medium. Cook fennel, shallots, and linguiça, stirring often, until fennel is softened and shallots are translucent, 5–8 minutes. Add wine, scraping up browned bits, and bring to a simmer. Add mussels, cover saucepan, and cook, shaking saucepan occasionally, until mussels open and are just cooked, about 5 minutes. Using tongs, transfer mussels to a bowl and tent with foil to keep warm; discard any that don’t open.

Step 2

Add potatoes to saucepan, cover, and cook until potatoes are tender, 12–18 minutes. Uncover and return mussels and any liquid accumulated in bowl to saucepan and toss to distribute.

Step 3

Ladle mixture into bowls along with any liquid in the bottom of the pot, top with fennel fronds, and drizzle with oil. Serve with lemon wedges.