Preheat oven to 415F (210C). Place bones in a baking dish and bake for 30 minutes, turning occassionally. Add tje carrot and onion and cook for an additional 20 minutes.  Allow to cool.

Put the bones, carrot and onion in a large heavy pan (I like my enameled cast iron pot) Drain the excess fat from the baking dish and pour 1 cup (250ml) of water into the dish. Stir to dissove the pan juices and little bits. Add to the beef mixture in the pan.

Add tomato paste ,celery and 10 cups (2.5 liters) of water. Bring to a boil. Skim the foam off the top as needed. Add the bouquet garni and peppercorns. Reduce heat and simmer 4 hours. Occasionally skim the foam off the top and give it a little stir.

Discard the bones and veggies. Ladle the stock in little batches into a fine sieve over a bowl. Press the solids down with the back of the ladle to get all the liquid out. Set the stock aside to cool. Refrigerate until cold and spoon off any fat that has risen to the top. Use within 48 hours or freeze for up to 6 months.