Preheat the oven to 375 degrees F. Grease a 9-by-13-inch baking dish with oil.
Brew the tea bags in 2 cups of hot water for 5 minutes. Discard the tea bags (don't squeeze them out).
Heat 3 tablespoons oil in a large skillet over medium heat. Add the onions and celery and cook, stirring frequently, until just soft, about 6 minutes. Add the mushrooms, sage, thyme, 1 1/2 teaspoon salt and a few grinds of pepper and cook, stirring, until the mushrooms are soft, about 4 minutes. Add the brewed green tea, then bring to a simmer and remove from heat.
Put the bread in a large bowl and pour in the green tea-vegetable mixture. Add the parsley and toss until the bread is completely coated. Let rest for 10 minutes so the bread can soak up the liquid. Gently toss again and transfer to the prepared baking dish. Drizzle with the remaining 1 tablespoon oil.
Cover with foil and bake for 30 minutes. Uncover and continue to bake until golden brown, about 15 minutes more. Serve hot.
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