I am not an expert but I see no reason you can't stew the whole chicken.
Don't boil the chicken. That will make it tough. Simmer. Braising (only a little broth or water) would be best. Put the broccoli and parsley in toward the end.
This recipe should give you the general idea. They don't use chicken, just broth. Just throw the chicken in at the start. Actually, put the breasts in a while after the other parts or they will dry out. Google for more recipes.
Here is a recipe of mine for chicken, yam and green bean curry. Here is another good recipe.