Scrub, rinse, and debeard the mussels. Spread the mussels in a single layer in a 13 x 9-inch heavy-duty aluminium foil pan. Pour 1/4 cup water over the mussels. Cover the pan with aluminium foil. Grill over Direct High heat until the mussels are opened, 5 to 6 minutes. Remove from the grill; chill mussels. Remove mussels from shells and discard one half of the shell.
To make the salad: In a large sauté pan, warm the oil and sauté the bell peppers, onions, and garlic for 2 to 4 minutes; add the squash and continue sautéing for 2 minutes. Remove from heat and add the remaining ingredients. Mix well and chill completely.
Place about 1 tablespoon ratatouille salad in each mussel shell and place the shell on a bed of kosher salt. Top each salad-filled shell with a chilled mussel. Sprinkle with coarsely chopped parsley.