Remove stems and seeds from the roasted green chiles.
Peel off as much of the skin as you can (you don't
have to get it all), and roughly chop into dime or
nickle sized pieces.
Place green chiles, chicken broth, garlic powder,
onion powder, oregano, and salt in a large sauce
pan. Mix everything well. Bring this mixture to
a low boil, reduce the heat to a simmer, and cook
over medium heat until the liquid is mostly gone.
Stir frequently, but be careful not to break up
the chiles too much.
Cook your burger as desired, top with a good amount
of the green chile mixture, and cover with American
cheese. Allow the cheese to melt well before placing
the burger on the bun. If I am cooking indoors,
I will add a little water to the pan and cover with
a pot lid to create a steambath to melt the cheese
(works very well).