Preheat the oven to 425 degrees F.
Prepare the scrubbed mussels for cooking by rinsing under running water. Discard any that are gaping, keeping only those that are firmly closed; also discard any that are very heavy.
Place the mussels in a pan with 2 to 3 tablespoons of dry white wine or water over medium-high heat and cook, stirring frequently, just until the mussels begin to open. (The mussels will continue cooking later.) With a slotted spoon, remove the mussels to a bowl as they open.
When all the mussels are removed, strain the liquid in the pot through a fine sieve or several layers of cheesecloth. Reserve the liquid. (You should have 1/4 cup of liquid - if not, make up the difference with a little dry white wine or water.) Remove the mussels from their shells, reserving a half shell for each mussel. Set the half shells on a baking sheet and place a mussel in each shell.
In a small bowl, combine the garlic, parsley, oregano, grated cheese, and bread crumbs, then sprinkle the mixture over the mussels in a thin layer. Drizzle the olive oil and reserved strained mussel liquid over the bread crumbs.
Bake the mussels for about 10 minutes or until the tops are brown and crisp. Serve piping hot or at room temperature. Do not reheat.