Season the Oxtail generously with Fleur de Sel and freshly cracked Black Peppercorns.
Heat Duck Fat in a large Dutch oven over medium-high heat. Brown the Oxtail in batches, ensuring not to overcrowd the pot. Set aside.
Add Yellow Onion, Carrots, and Celery to the Dutch oven and cook until softened and lightly caramelized, about 12-15 minutes.
Add Garlic and cook for another minute until fragrant.
Stir in Tomato Paste and cook for 3 minutes.
Deglaze the pot with Burgundy Red Wine, scraping up any browned bits from the bottom. Let the wine reduce by half.
Return the Oxtail to the Dutch oven. Add Veal Stock, Bay Leaves, and Fresh Thyme sprigs. Bring to a boil, then reduce heat to low, cover, and simmer for 5-6 hours, or until the Oxtail is extremely tender.
While the oxtail braises, prepare the Chestnut Purée: Steam or boil Chestnuts until tender. Peel while warm. Combine Chestnuts, Crème Fraîche, and Butter in a food processor and blend until smooth and creamy. Season with Fleur de Sel.
Prepare the Red Wine Jus: In a small saucepan, combine Red Wine, Red Wine Vinegar, and Shallots. Bring to a boil and reduce until syrupy.
Remove Bay Leaves and Thyme sprigs from the braise. Strain the braising liquid and reduce to a sauce consistency.
Serve the Oxtail with a generous spoonful of Chestnut Purée, drizzled with Red Wine Jus.
