I love to make a nice chicken soup.  I take some chicken legs, carrots, leak and celery, a few herbs and of course salt and pepper, and I just let it boil for like 4 hours. I then sift the soup to take out all the vegetables, skin, bones and meat. This way I get somewhat of a clear soup. Then I take the chicken and put in all the chicken meat back in to the soup. The thing is, I often have a hard time separating the chicken and vegetable "mash".  My question: is there an easier way to do this? I was thinking about putting the chicken in some kind of net, but couldn't find cooking nets online.  Are they maybe called different?  Is it an option to do half/half? Boil the chicken in 1 pan and the vegetables in a second one? 
Since the intermingling of the flavors is what your soup is about, and you want to remove only some of the solids (the chicken), a metal insert or colander might be too cumbersome.   Boil bags are what I’d suggest - cheap, disposable, and will allow everything to simmer together nicely.   https://www.amazon.com/dp/B071RJTTXH/ref=cm_sw_r_cp_api_i_8SdHCbFWV2C0R 