Pat the brisket dry and season both sides with salt and pepper.
Heat the olive oil in a skillet over medium-high heat. Brown the brisket on both sides, then transfer it to the slow cooker.
Add the sliced onion, celery pieces, and minced garlic around the brisket.
Pour the red wine and beef broth over the meat and vegetables.
Lay the thyme sprigs on top.
Cover and cook on low for 8 hours until the brisket is fork-tender.
Remove the brisket, slice it against the grain, and serve with the vegetables and cooking liquid spooned over the top.