If you're grinding your meat, place the defrosted meat in the freezer for 20 minutes to help firm it up, this will make it easier to grind and improve the texture. Cut the meat into large strips and run it through a grinder with a large die.
Take the ground meat and place it in a smoker (stovetop or outside) on low heat for 20 to 25 minutes using a hardwood like hickory or mesquite to add the smoke flavor. You don't want the meat to completely cook in the smoker, but you do want it to spend as much time as possible in the smoker, without having the meat start to brown, to let the smoke infiltrate the beef.
While the beef is in the smoker start cutting up the onion, celery, peppers, and garlic. The onion, celery, and peppers should be a large dice, so they hold up through the cooking process and to provide some crunch. The garlic should be finely minced.
In a large heavy duty pot sauté the vegetables in olive oil until they start to look translucent. Add the meat to the pan to brown. Once the ground beef is browned pour off the extra fat.
Add the beans, tomato paste, spice mixture, ketchup, BBQ sauce, Tabasco, Worcestershire sauce, lime juice, and liquid smoke to the pot. Add the tomatoes, breaking them up as you add them.
At this point, the chili should be thick, with just a little cooking liquid. If the chili is runny at this point add more tomato paste or ketchup to thicken it. As the chili cooks, it will release more liquid.
Bring the mixture to a boil, reduce the heat to a low simmer, cover and let cook for at least an hour. This is the type of food that will be better the longer and slower you let it cook.
As the chili cooks prepare the toppings. To make the chipotle sour creme mix the sour creme and ground Chipotle together. The cheese should be shredded using the coarsest shredder you have. The thicker pieces of cheese withhold their shape longer in the chili. Dice the green part of the green onions.
After the chili has cooked for at least an hour, season to taste. To serve, ladle into bowls laying down a small handful of cheese, with a spoonful of Chipotle sour cream on top, sprinkle green onions over the sour cream and chili.