Put oxtail, wine, port, cognac, celery, carrots, onions, garlic, juniper berries, bay leaves, and 2 sprigs of the thyme into a large bowl. Cover and let marinate in the refrigerator for 3 days.
Preheat oven to 300°. Strain marinade into a bowl and set aside. Set vegetables and aromatics aside in another bowl. Transfer oxtail to a clean surface, pat dry, then season with salt and pepper. Heat peanut oil in a large heavy ovenproof pot with a tight-fitting lid over medium-high heat. Working in batches, brown oxtail all over, 7–10 minutes per batch. Return oxtail to pot and roast in oven, uncovered, for 1 1⁄2 hours.
Reduce oven temperature to 250°. Transfer pot to medium heat on top of stove. Add reserved vegetables and aromatics and cook, stirring occasionally, until browned, 10–12 minutes. Stir in flour. Pour in reserved marinade, increase heat to high, and bring to a boil, skimming any foam that rises to the surface. Cover pot, transfer to oven, and braise, stirring occasionally, until meat is very tender, about 4 hours.
To make the tomato confit, heat olive oil in a small pot over medium heat. Add tomatoes, sugar, coffee, and remaining thyme. Simmer, stirring occasionally and reducing heat, if necessary, to prevent confit from boiling, until thick, about 1 hour. Season to taste with salt and pepper. Discard thyme. Keep confit warm over lowest heat.
Strain sauce from braised meat into a medium pot, skim off fat, and boil over medium-high heat, skimming occasionally, until reduced to 2 1⁄4 cups, 15–20 minutes. Meanwhile, pick meat off bones and return to large pot, discarding fat, sinew, bones, vegetables, and aromatics. Strain sauce through a sieve into pot with meat. Season to taste with salt and pepper. Keep warm over lowest heat.
Put 1 puff pastry circle on each pastry circle and spoon some of the sauce o top, then garnish each with a spoonful of the tomato confit.