Season the brisket on all sides with the smoked paprika, salt, and black pepper.
Place the brisket in the slow cooker and pour the barbecue sauce over the top.
In a bowl, toss the carrots, parsnips, sweet potatoes, and onion with the olive oil and minced garlic.
Arrange the vegetables around the brisket in the slow cooker.
Cover and cook on low for 8 hours until the brisket is fork-tender.
Remove the brisket, let it rest for 10 minutes, then slice or shred it.
Serve the meat with the vegetables and any sauce from the pot.