Step 1

Arrange a rack in the middle of the oven and heat the oven to 450°F.

Step 2

Rinse 4 pounds beef bones thoroughly under cold water and pat dry with paper towels. Place on a large rimmed baking sheet. Drizzle with 2 tablespoons canola oil and rub onto the bones to coat. Arrange into an even layer and roast until lightly browned, about 30 minutes.

Step 3

Meanwhile, cut 3 medium carrots and 3 medium celery stalks into rough 3-inch pieces. Peel and quarter 2 medium yellow onions. Smash and peel 3 large garlic cloves.

Step 4

Remove the baking sheet from the oven. Flip the bones. Nestle the carrots, celery, onions, and garlic around the bones, tossing to coat in the rendered fat. Dollop 2 tablespoons tomato paste in small spoonfuls into the rendered fat on the baking sheet (you do not need to spread the paste as it will distribute during the simmering).

Step 5

Return the baking sheet to the oven. Roast until the vegetables are caramelized in spots, the bones are a deeper brown, and the tomato paste has caramelized and is slightly darker in color, about 30 minutes.

Step 6

Meanwhile, trim the bottom 3-inches of stems from 1/2 bunch fresh parsley; reserve the tops for another use. Place the parsley stems, 8 fresh thyme sprigs, 3 dried bay leaves, and 1 tablespoon whole black peppercorns in the center of 8-inch-square piece of cheesecloth (do a double layer of cheesecloth if the weave is large) or inside a coffee filter. Fold up the sides of the cloth or filter and roll to create a parcel; tie tightly closed with kitchen twine.

Step 7

Bring a kettle or a small saucepan filled with about 1 cup water to a boil over medium heat. Meanwhile, transfer the roasted bones and vegetables to a large, deep stock pot with tongs or a slotted spoon. Carefully pour off the fat into a heatproof bowl (if you want to save it for another use, pour through a fine-mesh strainer and refrigerate).

Step 8

Pour the hot water onto the baking sheet and scrape up any browned bits from the bottom with a wooden spoon. Pour the pan juices and browned bits into the stockpot.

Step 9

Add enough cold water to the stockpot to just cover the bones and vegetables, about 3 quarts. Add 1/4 cup red wine vinegar and the herb bundle. Bring to a boil over high heat. Reduce the heat to low and gently simmer uncovered, skimming the surface as needed to remove any scum from the surface (no need to skim off the fat, as this is removed once chilled), until it has developed a rich color and body, at least 4 hours and up to 12 hours. Top up with water for only the first couple of hours to ensure that bones and vegetables are submerged. The longer it simmers, the deeper the flavor and color.

Step 10

Remove any large visible bones and the herb bundle with tongs or a spider (if you used meaty bones, you can pick off the meat for another use) and discard.

Step 11

Line a large fine-mesh strainer with a double layer of cheesecloth or a layer of opened-out coffee filters and fit over a large liquid measuring cup or large bowl. Strain the broth in batches, letting it strain naturally without pressing the solids. It is ok to stir gently, but be patient if you can! It will take longer to strain through coffee filters.

Step 12

Discard the contents of the strainer. Taste and season the broth with kosher salt as needed. If you want a deeper color, add 1 to 3 teaspoons soy sauce.

Step 13

To cool safely, add 1 cup ice cubes to the broth (it won’t weaken the flavor if you’ve simmered for a sufficient amount of time). Let cool for 30 minutes, then refrigerate for at least 3 hours or up to overnight. Once chilled, you can easily pick off the layer of solidified fat; discard or add to the rendered fat you already saved.