In a small bowl, stir together salt, paprika, and peppers; rub all over pork.
Place onion and garlic in a 5-quart slow cooker, and top with pork. Pour enough root beer around pork to cover by three-fourths.
Cover and cook on low until meat is tender, 6 to 8 hours. Remove pork from slow cooker, discarding cooking liquid. Shred pork with 2 forks, discarding fat and bone.
Return pork to slow cooker, and stir in barbecue sauce. Cover and cook on low until very tender and heated through, about 1 hour more.
Notes
Kitchen Tip: If you want to make this in advance, stop at step 3, and refrigerate the pork for up to 3 days. Continue with step 4 when you’re ready to eat.
Recipe by Paula Deen Magazine at https://pauladeenmagazine.com/root-beer-braised-pulled-pork-recipe/