Preheat the oven to 250 degrees F. Spread out the bread on 2 baking sheets; bake until dried out, about 1 hour, rotating the baking sheets as needed.
Increase the oven temperature to 350 degrees F. Melt the butter in a large pot over medium-high heat. Add the bacon and cook until crisp, about 8 minutes. Remove 1/4 cup of the drippings, leaving about 1/2 cup in the pot. Add the onion, celery, carrots and garlic and cook, stirring, until softened, about 4 minutes. Remove from the heat and add 1 1/2 cups stock. Add the marjoram and set aside.
Whisk the remaining 1 1/2 cups stock and the eggs in a large bowl. Add the scallions, parsley, Old Bay, oysters with their liquor and the vegetable-bacon mixture. Add the bread and mix until most of the liquid is absorbed. Season with salt and pepper.
Transfer the mixture to a 3-quart baking dish. Sprinkle with the parmesan and bake until browned on top, 30 to 40 minutes. Let sit 10 minutes before serving.