I made chili this past sunday with a bunch of leftover bbq I had frozen. I didn't use any pork but used brisket, beef rib meat, and a chuck steak.
I started out cooking 1 onion, and about 6 cloves of garlic with a little butter. Once the onions were nearly done I dumped in a bottle of beer, 1 can of whole peeled tomatoes and 2 6oz cans of tomato paste. Stirred it up and broke up the whole tomatoes in the pot and added the 2 seeded and steamed diced jalapenos, and 1 seeded and steamed diced green pepper. I let that get happy for about 10-15 minutes and then added in my leftover meats that I had previously chopped and diced. let that simmer for a while and then lastly add in your dry spices. I ended up using some 3-4 Tbls of Oakridge Black Ops Brisket rub. This makes a relatively thick chili, if you like a thinner chilli add another beer or add some chicken broth. You also could use water, but I figure if your gonna add something it might as well have some flavor profile with it.
When serving if you want to kick it up a notch heat wise just dash on some hot sauce. (My wife doesn't like super spicy chili like i do)