To make a vegan version of this stuffing, simply substitute a nondairy option for the butter and bake the stuffing in its own baking dish.
Spread bread cubes on two large baking sheets; let sit on the counter overnight, or bake in a 300-degree oven until just dried, about 15 minutes. Place in a large bowl.
In a large skillet, heat oil and butter over medium-high heat. Add mushrooms and cook, stirring frequently, until very tender, about 10 minutes. Stir in shallots and celery and cook 3 minutes longer. Stir in parsley, herbs, salt and pepper; remove from heat and spoon mixture over bread. Stir in broth and let sit a few minutes for it to be absorbed.
If using to stuff a turkey, cool completely and follow stuffing directions for your recipe. If baking separately, heat oven to 350 degrees. Spoon stuffing into a large buttered baking dish. Smooth the top and bake until browned and crisp, about 50 minutes.