Preheat oven to 350 degrees F.
In a saute pan, add the olive oil, carrot, onion, and celery with minced garlic and bay leaves. Heat mixture until the vegetables start to sweat. Sprinkle oxtails with salt and pepper and add to the vegetable mixture. Add the wine and cook for 10 to 15 minutes or until the wine evaporates. Add the cocoa and vegetable stock. Transfer mixture to a heatproof casserole.
Cover the casserole and bake in the oven slowly for 2 hours.
Check whether there is too much stock remaining and if so, turn up heat until excess stock evaporates. Add the tomatoes and cook for 40 minutes with cover on. Check and stir occasionally.
To make the garnish: Place the water in a saucepan and bring to a boil. Clean and cut the carrots and celery into 1/4-inch julienne sticks. Salt the water and cook the celery and carrot sticks together al dente, about 2 minutes. Drain. Saute the vegetables with extra- virgin olive oil, salt, and pepper.
Remove pieces of oxtail from the casserole, and put them in a warming dish. Take the sauce that is left in the casserole dish and pass it through a blender.
To serve: place the oxtail pieces on plates and cover generously with the sauce. On the top, place the carrots and celery garnish, and decorate with the chopped basil leaves.