Mix together the tomato paste, vegetable oil, chili powder, cumin, garlic and onions in a microwave-safe bowl. Cover the top of the bowl with a very wet paper towel. Microwave for 5 minutes. Transfer the mixture to a slow cooker.
Add the pork to the slow cooker along with the stock, adobo sauce, salt, beans and 1 cup of the BBQ sauce. Cook on high until the pork is cooked through and tender, 4 to 5 hours (or on low for 6 to 8 hours). Skim any excess fat off the top and discard. Adjust the seasoning if necessary.
In a small bowl, mix together the sour cream, garlic powder and remaining 1/4 cup BBQ sauce.
Top the chili with the sour cream mixture, pork rinds and scallions. Serve with the chips on the side or crumbled on top.
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