Add the clams, tossing gently for about 1 minute. Pour the wine over the clams. Cover the pot and let the clams steam for 3 minutes.
At the 3 minute mark, give the clams another toss, checking to ensure the garlic is not scorching. Replace the lid and continue to steam. Depending on the size of the clams and the heat of the grill, the clams will start to open after 5 to 10 minutes. As each clam opens, pull it out of the pot with tongs, setting it aside until all the clams have opened.
While the broth is still in the Dutch oven, taste it for seasoning. It may need a pinch of salt. Once the seasoning is adjusted, fold the parsley into the hot broth and add the clams back in for about 30 seconds. Pour the contents of the Dutch oven into a bowl and enjoy.