Pat the short ribs dry and season all over with salt and pepper.
Heat the olive oil in a large skillet over medium-high heat. Sear the ribs in batches for 3 to 4 minutes per side until deeply browned, then transfer to the slow cooker.
In the same skillet, cook the onion, carrots and celery for 4 to 5 minutes until the onion softens.
Stir in the garlic and tomato paste and cook 1 minute until fragrant.
Pour in the red wine, scrape up the browned bits from the pan, and let it bubble for 2 minutes.
Pour the wine and vegetables over the ribs. Add the beef broth, Worcestershire sauce, thyme and bay leaves.
Cover and cook on low for 8 hours, or on high for 4 to 5 hours, until the meat is fall-off-the-bone tender.
Remove the ribs and keep warm. Strain the sauce into a saucepan, skim the fat, and simmer 5 to 10 minutes to reduce slightly. Whisk in the cornstarch slurry if a thicker sauce is wanted, and simmer 1 to 2 minutes until glossy.
Serve the ribs over mashed potatoes with the sauce spooned over the top, scattered with parsley or chives.