I took 3 pounds of salt and peppered pork neck bones (used to get them for $.50 a pound, now $1.99, still good) and browned them off in an enameled cast iron pot with a couple tablespoons of olive oil. I then removed them and added a chopped onion, a rib of chopped celery, and a chopped carrot and let them begin to caramelize (also added a little more salt and pepper). I then broke up and added a 28 ounce can of tomatoes to the pot with its juices. I added 2 dried bay leaves, 1.5-2 tablespoons of Hungarian paprika, 4-10 (depending on size and taste) cloves of garlic, and a can of chicken/beef broth to the pot. After that I returned the neck bones to the mixture followed by bringing it to a light boil, putting the lid on, reducing the heat to low, and then letting it simmer for 2-3 hours.
Once it was done I let it cool and then refrigerated it for 4-8 hours to let the fat collect at the top. I chopped another onion, another rib of celery, 2 more cloves of garlic, and another carrot and sautéed them in a small amount of the fat with a bit of salt and pepper. The next steps I took were to heat up the previously cooled ingredients, remove the neck bones, strain the vegetables, and then add the liquid to the newly sautéed aromatics and then to reduce for about 5 minutes. In the mean time I stripped the meat off the bones and tried to remove the fattier parts. I then added the meat to the broth. I tested it for seasoning, it was perfect. I then served my family parts of the soup that were heavy in the meat and vegetables, and a little light on the broth. I saved more of the broth for myself. I selfishly drank the broth which was indescribably delicious. I didn't care about any other part of the soup, just the broth. My family was happy too.
When I reach near death and require an IV, I request that it be filled with this liquid, it will allow me to die happy.
A similar method works well with bone-in country ribs or any cheap bone-in piece of pork.
May I suggest a small improvement? Get rid of the canned chicken/beef broth. Replace it with water, salt and/or MSG to taste (which is basically all that's in your canned broth). Or better yet, homemade broth. Making a broth with canned broth as an ingredient seems like a step in the wrong direction. Otherwise, this all sounds tasty.