Scrub the clams under cold running water, discarding any that fail to close to the touch. In a large bowl, combine the clams, a handful of coarse salt and enough water to cover the clams. Let stand for at least 30 minutes or up to 2 hours so that the clams release any sand trapped in their shells. Drain and set aside the clams.
Then, in a deep skillet, heat the olive oil over medium-high heat. Add the onions and garlic and saute, stirring often, until golden, about 1 minute. Sprinkle in the paprika and breadcrumbs and saute a couple of minutes longer, until the ingredients are very fragrant and golden. Add the clams, white wine and clam broth. Cover and let steam for a few minutes, just until the clams open. Discard any clams that don't open.
Check the broth for seasoning. Sprinkle with the parsley and serve the clams with their broth and some crusty sourdough bread on the side. Lemon wedges are optional.