Brown Beef Stock

Heat oven to 400 degrees.

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, until beginning to brown, about 45 minutes. Remove from oven, add tomato paste, and stir to combine. Cook over medium heat for about 30 seconds (to let it brown a little, which cooks out some of the acidity and intensifies the sweetness), 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. Set the pan over two burners. Add water and bring to a boil, scraping up any brown bits from bottom with a wooden spoon. Boil until liquid is reduced by half, about 3 minutes. Pour contents of pan into the stockpot.

Add enough water to stockpot to cover bones and vegetables by 2 inches (about 6 quarts). Bring to just under a boil, then reduce heat to a bare simmer (bubbles should just gently break at the surface). Add herbs and peppercorns and very gently simmer, uncovered, over low heat for 8 hours, adding more water as necessary to keep everything submerged.

Carefully pour stock through a cheesecloth-lined sieve (do not press on solids) into a large heatproof bowl or another stockpot; discard solids. Stock will be dark brown. Skim off fat if using immediately or let cool completely (in an ice water bath, if desired) before transferring to airtight containers. Refrigerate at least 8 hours to allow the fat to accumulate at the top; lift off and discard fat before using or storing.