Rinse the cockles, then to purge any sand, soak them in a large bowl of cold water with 2 tablespoons coarse salt. Let them sit for 30 minutes, changing the water if you see sand, then drain well.
Mince 2 large garlic cloves and chop a few sprigs of fresh parsley, reserving some parsley for garnish.
Heat 2 tablespoons extra-virgin olive oil in a large pot over medium heat. Add the garlic and sauté for 1 minute, being careful not to let it brown.
Add the drained cockles and 1/2 cup dry white wine, then increase heat to high and cover the pot.
Steam for 3 to 5 minutes, shaking the pot occasionally, until all the cockles have opened. Discard any that remain closed.
Divide the cockles between a serving dish or individual plates, ladle over the cooking liquid, sprinkle with the reserved parsley, and serve with lemon wedges, if desired.