Season the beef cheeks generously with salt and pepper. Heat the olive oil in a large Dutch oven or heavy pot over medium-high heat. Once hot, add the beef cheeks and sear on all sides until browned. Remove the beef and set aside.

In the same pot, add the diced onion, carrots, and celery. Sauté for about 5-7 minutes until the vegetables are softened. Add the minced garlic and crushed fennel seeds, cooking for an additional minute until fragrant.

Pour in the red wine, scraping the bottom of the pot to release any browned bits. Allow the wine to simmer for about 2-3 minutes until slightly reduced.

Return the beef cheeks to the pot. Add the beef broth, thyme sprigs, and bay leaf. Bring the mixture to a gentle simmer, then cover and reduce the heat to low. Let it braise for about 2.5 to 3 hours until the beef is tender.

While the beef is cooking, preheat the oven to 400°F (200°C). On a baking sheet, toss the chopped potatoes, parsnip, and turnip with a drizzle of olive oil, salt, and pepper. Roast in the oven for 25-30 minutes or until golden and tender.

Once the beef is tender, remove it from the pot and set aside. Discard the thyme and bay leaf. Use an immersion blender to blend the cooking liquid until smooth. Stir in the balsamic vinegar, adjusting seasoning with salt and pepper if needed.

Slice the beef cheeks and serve them on a plate with the roasted root vegetables. Drizzle the rich gravy over the top for an indulgent finish.