Cut the challah into 1" cubes. Leave the cubes out on a parchment lined sheet pan on the counter to get stale, at least overnight, and preferably 2 days.
Melt 3 oz. of butter in a large heavy saute pan. Saute the onions until wilted, add the herbs, celery and mushrooms and cook until just slightly cooked through.
In a large bowl, combine bread cubes, vegetables, melted butter and vegetable stock, and salt and pepper. Test for seasoning and adjust.
Press stuffing into a large buttered baking dish. Cover with buttered parchment, and then foil. At this point, the stuffing can be held for several hours, but should be at room temperature before baking.
Bake at 350 for 45-55 minutes, the last 10-15 minutes without the foil and parchment, to crisp the surface.