Clean the mussels thoroughly under cold running water. Scrape off any barnacles with a small knife and pull out the "beard" (byssus) that hangs from the shell. Discard any mussels that are broken or do not close when tapped.
For the strict Neapolitan 'Mpepata:
Place the clean mussels directly into a large, dry, hot pot over high heat. Do not add oil, water, or wine.
For the Cozze alla Marinara:
Heat the extra virgin olive oil, crushed garlic, and parsley stalks in a large pot over medium heat until fragrant. Increase the heat to high, add the mussels, and pour in the dry white wine immediately.
Cover the pot with a lid immediately to trap the steam. Cook for about 3 to 5 minutes until the shells open.
Shake the covered pot or use a large spoon to mix the mussels gently once or twice to ensure they cook evenly.
Deglaze with white wine and let it evaporate
Remove the pot from the heat as soon as the shells have opened. Discard any mussels that remain closed.
Transfer the cooked mussels to a serving bowl.
Filter the cooking liquid remaining in the pot through a fine-mesh sieve or cheesecloth. This is crucial to remove any sand or impurities released by the shells.
Pour the hot, filtered broth back over the mussels.
Sprinkle generously with freshly ground black pepper. If you made the Marinara version, add the fresh chopped parsley leaves now.
Serve immediately with lemon wedges and slices of toasted bread.