Steps

1. Clean the mussels and clams under cold running water, discarding any with cracked shells or shells that don’t close when they’re tapped. Scrub the shells well and pull out any clumps or threads that have gathered at the hinges of the shells with a pair of pliers.
2. Preheat the grill to high.
3. Put the wine in a small saucepan over medium heat with the shallots and allow it to slowly reduce by about one-half. Add the butter, salt, and pepper, and cook until the butter has melted. Remove from heat and keep warm.
4. Use a fish or vegetable grate if you have one for your grill. Preheat it for 5 minutes before adding the mussels and clams to the grate (or place them directly on the grill grate), rounded side down. Grill until the shells open, 2 to 5 minutes for the mussels, or 5 to 8 minutes for the clams. Cooking times will be slightly longer if the grill is uncovered; remove the bivalves as they open.
5. Brush the bread slices with olive oil and place on the grill to toast while you sauce the bivalves.
6. Put the mussels and clams together in a large serving bowl, being careful to remove any that haven’t opened. Drizzle the shallot-butter sauce over the top and sprinkle with the parsley leaves. Stir from the bottom, to distribute the sauce and parsley. Serve with the crusty grilled bread.