In a large Dutch oven, heat olive oil over medium-high heat. Add the short ribs and sear until browned on all sides, about 8-10 minutes. Remove the ribs and set aside.

Sauté the Vegetables

In the same pot, add carrots, onion, celery, and garlic. Sauté until softened, about 5 minutes.

Deglaze

Pour in the red wine, scraping the bottom of the pot to release any browned bits. Bring to a simmer.

Add Broth and Herbs

Return the short ribs to the pot. Add beef broth, thyme, and bay leaves. Bring to a boil, then reduce heat to low.

Braise

Cover and braise the short ribs for 2.5 to 3 hours, or until the meat is tender and falling off the bone.

Cook the Potatoes

In a separate pot, boil the Yukon Gold potatoes until fork-tender, about 15-20 minutes. Drain and return to pot with butter, mashing until smooth.

Serve

Remove the short ribs from the pot and let rest for a few minutes. Serve the ribs over mashed Yukon Gold potatoes, garnished with chopped parsley.