Preheat the oven to 400 F.
Arrange bones and short ribs in a single layer in a large, heavy roasting pan. Drizzle with oil and turn to coat. Roast, turning once and stirring often for even browning, about 45 minutes. Remove from oven, add tomato paste, and stir to combine. Cook over medium heat for about 1 minute, then add vegetables, stirring well. Return to oven and roast until vegetables are browned and tender and bones are deeply browned, about 40 minutes.
Transfer bones and vegetables to a large stockpot, then spoon off fat from roasting pan and discard.
Add enough water to stockpot to cover bones and vegetables by 2 inches. Bring to just under a boil, then reduce heat to a bare simmer (bubbles should just gently break at the surface). Add peppercorns, parsley, thyme, and bay leaf, then continue to simmer, uncovered, over low heat for at least 3 hours. For more flavour, simmer up to 8 hours. Add more water as necessary to keep everything submerged.
Carefully pour stock through a cheesecloth-lined sieve into a large heatproof bowl or another stockpot; discard solids. Stock will be dark brown. Put into large Cambro or any container large enough to fit all the stock. Refrigerate at least 8 hours to allow the fat to accumulate at the top; lift off and discard fat before using or storing.
Store in fridge for up to 3 days or in freezer for up to 3 months.
*Double Short Ribs if unavailable
** Sub for water if desired