Purge the cockles by soaking them in cold water with 2 tablespoons of coarse sea salt for 30 minutes, changing the water if it becomes sandy. Drain well.
Finely chop 2 large garlic cloves and a few sprigs of fresh parsley, reserving some parsley for garnish.
Heat 30ml extra virgin olive oil in a large pan over medium heat. Add the chopped garlic and cook for 1 minute, stirring, until fragrant but not browned.
Add the drained cockles and 100ml dry white wine. Increase the heat to high and cover with a lid.
Cook for 3–5 minutes, shaking the pan occasionally, until all the cockles have opened. Discard any that remain closed.
Transfer the cockles to a serving dish or individual bowls with the cooking juices. Sprinkle with the reserved parsley and serve with lemon wedges, if you like.