Arrange bones on 2 rimmed baking sheets and roast, turning occasionally, until well browned, about 45 minutes. Transfer bones to a 12-quart stockpot. Pour off fat from baking sheets, reserving 1 tablespoon. Add water and vinegar to pot and bring to a boil. Reduce heat and gently simmer, skimming off foam occasionally, 1 1/2 hours.
Meanwhile, arrange onions, carrots, celery, and garlic on baking sheet (from roasting bones) and drizzle with reserved fat. Roast vegetables, tossing occasionally, until softened, about 40 minutes.
Add vegetables to pot with bones, then stir in parsley, thyme, bay leaves, peppercorns, and mushrooms. Keep heat low enough that liquid barely simmers, and cook 12 hours (overnight).
Strain soup through a fine-mesh sieve and discard solids. Skim any remaining foam and taste broth. To intensify flavor, transfer soup to a clean pot and boil to desired concentration.