Purchase mussels and plan on using them the same day or at the latest, the next. Upon bringing them home from the market, remove any packages, and place into a bowl. Place a damp towel on top of them loosely, but directly, and leave in the refrigerator until you are ready to cook them.
Chop the onion, shallot and garlic. Place a large skillet or Dutch oven on the stove top at medium heat (make sure it has a lid that fits it well). Place the chopped onion, shallot and garlic into the skillet/Dutch oven and cook until tender, but not translucent.
While the aromatics are cooking, prepare the moules (mussels). See directions in the ingredient list. Before adding the moules, add both the heavy cream and wine. Let the sauce reduce down for about five minutes at medium, to medium-high heat. Then add the moules, cover the skillet, and steam for about 5-7 minutes until they open. If after 10 minutes any moules do not open, discard them.
Remove the moules from the Dutch oven/skillet, and place in a serving bowl. Pour the sauce over the moules and sprinkle with parsley.
Serve with fresh bread, a glass of your favorite wine, perhaps the white wine you used to cook the moules with, and enjoy.