Preheat your oven to 325°F (163°C).

In a large Dutch oven, heat olive oil over medium-high heat. Season the brisket generously with salt and pepper. Once the oil is hot, sear the brisket on all sides until browned, about 4-5 minutes per side. Remove the brisket and set it aside.

In the same pot, add the diced onion and sauté until translucent, about 5 minutes. Add the minced garlic and cook for an additional minute until fragrant.

Pour in the balsamic vinegar and beef broth, scraping the bottom of the pot to deglaze it. Stir in the brown sugar and add the fresh thyme. Bring the mixture to a simmer.

Once simmering, add the chopped carrots, parsnips, and diced potato to the pot. Stir to combine.

Return the seared brisket to the pot, nestling it among the vegetables. Cover the pot with a lid and transfer it to the preheated oven.

Braise the brisket for about 3-4 hours, or until the meat is tender and easily pulls apart with a fork.

Once the brisket is done, remove it from the pot and let it rest. Strain the braising liquid and vegetables through a fine mesh sieve into a saucepan. Use a blender to purée the vegetables until smooth, then return the mixture to the saucepan. Heat the gravy over medium heat, adjusting seasoning with salt and pepper to taste.

Slice the brisket against the grain and serve it drizzled with the velvety root vegetable gravy.