1 Roast the meat, bones, and vegetables: Preheat oven to 400°F. Rub a little olive oil over the stew meat pieces, carrots, and onions. Place stock bones, stew meat or beef scraps, carrots and onions in a large, shallow roasting pan.
Roast in oven for about 45 minutes, turning the bones and meat pieces half-way through the cooking, until nicely browned. If bones begin to char at all during this cooking process, lower the heat. They should brown, not burn.
When the bones and meat are nicely browned, remove them and the vegetables and place them in a large (12 to 16 quart) stock pot.
2 Add hot water and scrape up the browned bits: Place the roasting pan on the stove-top on low heat (will cover 2 burners), pour 1/2 cup to a cup of hot water over the pan and use a metal spatula to scrape up all of the browned bits stuck to the bottom of the pan.
Pour the browned bits and water into the stock pot.
3 Add vegetables, water, bring to a low simmer: Add celery tops, garlic, parsley, bay leaves, and peppercorns to the stock pot.
Fill the stock pot with cold water, to 1 to 2 inches over the top of the bones. Put the heat on high and bring the pot to a low simmer and then reduce the heat to low.
If you have a candy or meat thermometer, the temperature of the water should be between 180° and 200°F (boiling is 212°F). The stock should be at a bare simmer, just a bubble or two coming up here and there. (You may need to put the pot on your smallest burner on the lowest temp, or if you are using an oven-safe pot, place it in the oven at 190°F.)
Cover the pot loosely and let simmer low and slow for 3-6 hours.
Do not stir the stock while cooking. Stirring will mix the fats in with the stock, clouding up the stock.
4 Skim scum and fat: As the stock cooks, fat will be released from the bone marrow and stew meat and rise to the top. From time to time check in on the stock and use a large metal spoon to scoop away the fat and any scum that rises to the surface.
(Do not put this fat down your kitchen drain. It will solidify and block your pipes. Put it in a bowl or jar to save for cooking or to discard.)
5 Remove solids and strain: At the end of cooking time (when you want to end the cooking is up to you, 3 hours minimum, 6 to 8 hours if you can do it) use a slotted spoon or spider ladle to gently remove the bones and vegetables from the pot (discard them, though if you see a chunk of marrow, taste it, it's delicious).
Line another large pot (8-quart) with a fine mesh sieve, covered with a couple layers of cheesecloth if you have it.
Pour the stock through the sieve to strain it of remaining solids.
6 Chill: Let cool to room temperature then chill in the refrigerator.
One the stock has chilled, any fat remaining will have risen to the top and solidified. The fat forms a protective layer against bacteria while the stock is in the refrigerator. If you plan to freeze the stock however, remove and discard the fat, pour the stock into a jar or plastic container. (You can also remove the fat, and boil the stock down, concentrating it so that it doesn't take as much storage space.) Leave an inch head room from the top of the stock to the top of the jar, so that as the stock freezes and expands, it will not break the container.