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Preheat oven to 300º. Whisk miso, oil, and 2 Tbsp. water in a small bowl. Crush mushrooms and kombu with your hands over a rimmed baking sheet. Add onions, carrot, celery, garlic, and parsley and toss to combine. Drizzle miso mixture over vegetable mixture and toss to coat. Bake, tossing halfway through, until vegetables are slightly shriveled and mixture is fragrant, 60–75 minutes.
Transfer vegetable mixture to a large pot. Add peppercorns and 4 quarts cold water. Bring to a boil, then reduce heat and simmer, uncovered and stirring occasionally, until broth is reduced by half, 60–75.
Let broth cool, then strain through a fine-mesh sieve into a large bowl, pressing on solids to extract as much liquid as possible; discard solids.
Do Ahead: Broth can be made 3 days ahead. Let cool; cover and chill, or freeze up to 3 months.