Prepare carrots by scrubbing off any dirt or peeling and roughly chopping.
Prepare celery by washing and roughly chopping - extra leaves can be added.
Remove outer skins and chop the onion in half and then into quarters.
Place all vegetables in the bottom of your slow cooker.
Remove pork from the package and leave on any strings. Using tongs place roast on a plate and rotate to sprinkle with salt and pepper.
Heat large dutch oven or other heavy duty pot on the stove on medium high heat. Wait a minute or 2 and add enough canola oil to lightly line the bottom of the pot.
Add pork and brown on all sides - including the ends. Pork should release to rotate when it is brown. Use oven mitts and tongs as the oil will splatter.
Place browned roast on top of vegetables in the slow cooker.
Reduce heat on your stove to low. Slowly pour in half the beer and scrape up any brown bits.
Pour the contents of your dutch oven into the slow cooker along with the remaining beer.
Cover and cook on auto shift (which is high then low for a total of 8 to 10 hours on most slow cookers). If you are home rotate the roast half way through the cooking time.
At least 30 minutes before dinner time remove the roast from the slow cooker onto a cutting board. Turn off slow cooker.
Place a strainer over a medium sized bowl and using oven mitts pour the remaining contents into the strainer. Reserve 1 cup of the liquid and add back into the slow cooker. Vegetables and remaining broth can be discarded.
Remove any string from roast and discard. Using a knife and a couple of forks shred the meat until the roast is pulled apart. Discard any fat or bones and put meat back into the slow cooker.
Mix meat together with broth and 1 cup of BBQ sauce. Turn slow cooker to warm until ready to serve.