Drying sourdough bread out in the oven ensures that it absorbs all the delicious flavors in this vegan Thanksgiving stuffing/dressing, while drizzling with vegetable broth keeps it perfectly moist.
Preheat oven to 300 degrees. Divide bread between two rimmed baking sheets and spread in a single layer. Bake, stirring a few times, until crisp and dried all the way through, 30 to 40 minutes. Transfer to a large bowl.
Heat 5 tablespoons oil in a large skillet over medium-high. Add mushrooms, 2 teaspoons salt, and 1/4 teaspoon pepper; cook, stirring occasionally, until tender and beginning to brown, about 8 minutes. Transfer to bowl with toasted bread. Heat remaining 2 tablespoons oil in same skillet. Add leeks, celery, and thyme sprigs; cook until vegetables are softened, about 4 minutes. Add garlic, chopped thyme, and red-pepper flakes; cook 1 minute. Add 1/2 cup broth and cook, scraping up browned bits from bottom, until evaporated, 1 to 2 minutes. Discard thyme sprigs. Transfer to bowl with bread; let cool 5 minutes. Meanwhile, brush a 2- to 2 1/2-quart baking dish with oil.
Increase oven temperature to 375 degrees. Add parsley to bowl with bread; toss to combine. Slowly drizzle with remaining 1 1/2 cups broth, stirring to moisten. Transfer to prepared baking dish. Loosely cover with parchment-lined foil. Bake 20 minutes. Uncover; continue baking until golden on top, 25 minutes more. Serve, sprinkled with more parsley if desired.