Grilled Mussel and Potato Salad

1 lb small (1 1/2-inch) red boiling potatoes
6 tablespoons extra-virgin olive oil
1/4 cup fresh lemon juice
2 lb mussels (preferably cultivated), cleaned but not steamed
1 fennel bulb (sometimes called anise; 1 lb), stalks discarded and
bulb halved and very thinly sliced
1/2 cup finely chopped fresh flat-leaf parsley
1/3 cup brine-cured black olives, pitted and chopped
1 tablespoon drained bottled capers
Special equipment: a disposable aluminum baking pan (at least 1
inch deep)

Cover potatoes with salted water by 1 inch in a large saucepan, then simmer, uncovered, until just tender, about 15 minutes. Drain in a colander and rinse under cold water until cool.

Prepare grill for cooking.

Cut cooled potatoes crosswise into thirds and arrange in 1 layer on a tray. Brush both sides of potatoes with some oil (2 tablespoons total for all of them) and season with salt and pepper.

When fire is medium-hot (you can hold your hand 5 inches above rack 3 to 4 seconds), grill potatoes on lightly oiled rack until grill marks form, about 1 minute on each side, then transfer to a large bowl. Toss hot potatoes with 2 tablespoons lemon juice.

Put mussels in aluminum pan and cook in covered grill, stirring occasionally, 5 to 6 minutes, or until they just open. Transfer mussels to a bowl with a slotted spoon. Discard any that haven't opened, then shuck remainder.

Add mussels to potatoes along with fennel, parsley, olives, capers, and remaining 2 tablespoons lemon juice, tossing to combine, then let stand at room temperature, tossing occasionally, 10 minutes.