Combine the chicken wings, beef bones, carrot, celery, onion and bay leaf in a medium saucepan. Cover with cold water to a depth several inches above the ingredients. Bring to a boil.
Lower the heat and simmer slowly, skimming off any scum that rises to the top during the first few minutes. Continue to cook at a slow simmer, partially covered, for an hour or longer, until the broth looks rich and golden. Season to taste with salt and pepper.
Cool the broth until warm, and strain into a bowl or another saucepan. The broth can be used immediately or, if time permits, chilled; afterwards, scoop off any fat that has solidified on top. The broth will keep, refrigerated, for up to a week, or freeze it in 1- or 2-cup containers.