Heat the olive oil in a skillet over medium heat until the oil shimmers. Add the mushrooms and cook until the mushrooms are very soft (but not in a mushy way).
Stir in the shallots and the garlic and cook until fragrant. Add the white wine, herbes de Provence, and whatever water that comes from draining the oysters, stirring as you add the wine. Lower the heat a little and cook, stirring now and then, until thickened to a moderately wet stuffing texture. Remove from heat and stir in the parsley, basil, salt and pepper.
Remove the stuffing from the pan and allow to cool. If you are ready to cook and serve the oysters, shuck them and put them either on their shells or in a small gratin dish, then go directly to Step 5.
If you're making the stuffing in advance, when they're cool put them into a food storage bag or plastic container and refrigerate.
When you're ready to cook, preheat the oven to 425 degrees. Using shells or gratin dishes, top each oyster with a heaping tablespoon of the stuffing. Put the shells on a metal tray of rock salt (to keep the shells from rocking and sliding), and put the tray into the oven. (If using gratin dishes, place them on a metal tray without the salt). Bake at 425 degrees for about ten minutes, or until the sauce is bubbling and beginning to brown. Serve very hot.