1Preheat oven to 350ºF. Lightly spray a 9 x 13-in baking dish with nonstick cooking spray or line with parchment paper. Place bread cubes in a large bowl.
2In a large, heavy-bottomed saucepan over medium heat, cook onions, celery, mushrooms, 1/4 cup vegetable broth or water, liquid aminos (or shoyu), and pepper, stirring frequently, until vegetables are softened, about 10 minutes.
3Whisk in remaining vegetable broth, roasted garlic, sage, and thyme. Bring to a simmer, then remove from heat.
4Pour broth and vegetables over bread cubes. Mix thoroughly. Transfer stuffing to prepared baking dish. (The stuffing can be assembled up to one day in advance. Cover with aluminum foil and refrigerate. Let come to room temperature before baking as directed.)
5Cover dish with foil and bake for 25–30 minutes. Remove foil and bake until top crisps slightly, 5–10 minutes.