Preheat your oven to 300°F (150°C).

In a large Dutch oven or heavy pot, heat the olive oil over medium-high heat. Season the short ribs with salt and pepper, then add them to the pot. Sear the ribs on all sides until browned, about 3-4 minutes per side. Remove the ribs and set them aside.

In the same pot, add the leeks, carrots, parsnips, onion, and garlic. Sauté for about 5-7 minutes, until the vegetables are softened and the leeks are slightly charred.

Stir in the smoked paprika, thyme, and rosemary, and cook for an additional minute until fragrant.

Pour in the red wine, scraping the bottom of the pot to deglaze and remove any browned bits. Allow the wine to simmer for about 2-3 minutes.

Add the beef broth and tomato paste to the pot, stirring well to combine. Bring the mixture to a simmer.

Return the short ribs to the pot, ensuring they are submerged in the liquid. Cover the pot with a lid and transfer it to the preheated oven.

Braise the short ribs in the oven for 3-4 hours, or until the meat is tender and falling off the bone.

Once cooked, remove the pot from the oven. Carefully take out the short ribs and set them aside on a plate.

Skim any excess fat from the surface of the liquid, then return the pot to the stove. Simmer the gravy over medium heat for about 10-15 minutes, or until it has thickened to your liking.

Taste and adjust the seasoning with salt and pepper if necessary.

Serve the short ribs topped with the rich root vegetable gravy and garnish with fresh parsley.