Pat the beef shank dry with paper towels and season both sides evenly with the sea salt and black pepper.
Heat the extra virgin olive oil in a heavy-bottomed pot or Dutch oven over medium-high heat.
Sear the beef shank for 4-5 minutes per side until a deep golden-brown crust forms, then remove it from the pot and set aside.
Add the chopped yellow onion, sliced carrots, and sliced parsnips to the same pot, sautéing for about 5 minutes until the vegetables begin to soften.
Stir in the minced garlic and tomato paste, cooking for 1 minute until the mixture becomes fragrant and slightly darkened.
Pour in the beef broth and add the dried thyme, using a wooden spoon to scrape the bottom of the pot to release any flavorful browned bits.
Return the beef shank to the pot, ensuring it is partially submerged in the liquid, and cover with a tight-fitting lid.
Reduce the heat to low and simmer gently for 2 to 2.5 hours, or until the meat is fork-tender and easily pulls away from the bone.
Serve the beef shank hot in a shallow bowl, surrounded by the braised root vegetables and a generous spoonful of the reduced cooking liquid.