Gently scrap brown gills from inside of each mushroom cap. Lightly wipe with damp papertowel. Rub each cap with a little olive oil and set aside.
Toast bread cubes until golden brown on baking sheet, and remove to a large bowl.
Heat butter over medium high heat in a large skillet, add onions and celery and cook, stirring, about 5 minutes until tender.
Remove from heat and stir in parsley and other spices. Stir in stock and eggs.
Stir in bread cubes, and chopped oysters and toss well until stuffing is moist but not packed together.
Remove approximately 4 cups stuffing and place in food processor. Pulse until mixture is finely chopped and comes together slightly, about 30 seconds. Repeat if necessary so you have about 3 cups of chopped stuffing.
Reserve remaining stuffing and place in small casserole dish. Refrigerate for later use.
Divide the stuffing among the mushroom caps, and 1/2 cup for each mushroom. Place filled mushrooms on a baking sheet.
Bake until golden brown on top and mushrooms are tender, about 15 to 18 minutes. Garnish with remaining 2 tablespoons minced parsley.