I've long been a big fan of making my own chicken stock - I'll use backs when I am buying whole chickens to cut up, and will save bones and bits of meat after making roast chicken. Often I can see a bunch of what looks like good meat while I'm straining out the stock, and I've been interested in trying to make food out of it - essentially making the chicken work double duty, first in stock making and then in something to eat.
Has anyone tried this? I've seen some recipes where you will use chicken to make broth for chicken soup, and then put the meat in the soup, but I'm concerned that once broth or stock is made, the chicken won't be very good anymore - since so much of the flavor will have cooked out. When I'm making poached chicken - for tinga poblana, for example - the poaching water never seems to have enough ooomph to it to really be used for a broth.
So - I guess I'm just wondering if it's possible to balance it in such a way that both work - cook long enough to have a good broth, but short enough that the chicken can be shredded and cooked in enchiladas or served in some sort of sauce.