Preheat the oven to 300°F (150°C). Season the short ribs with salt and black pepper. In a large Dutch oven, heat olive oil over medium-high heat. Sear the short ribs on all sides until browned. Remove and set aside.

Sauté Vegetables

In the same pot, add onion, carrots, and celery. Sauté for about 5 minutes until softened. Add minced garlic and cook for an additional minute.

Deglaze and Braise

Pour in the red wine, scraping the bottom of the pot. Bring to a boil and reduce by half. Return the short ribs to the pot, add beef broth, thyme, and bay leaves. Bring to a simmer, cover, and transfer to the oven. Braise for 3 hours until the meat is tender.

Make the Smashed Potatoes

While the ribs are braising, boil the potatoes in salted water until tender, about 15-20 minutes. Drain and return to the pot. Add butter, milk, salt, and mash until smooth.

Roast the Broccoli

Toss the broccoli florets with olive oil, salt, and pepper. Spread on a baking sheet and roast in the oven for 15-20 minutes until tender.

Finish the Dish

Once the short ribs are tender, remove from the oven and let rest for 10 minutes. Serve with smashed potatoes, roasted broccoli, and drizzle with demi-glace.