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Drizzle beef with 1 tablespoon of the oil, and sprinkle with lots of salt and freshly ground pepper. Stir to coat.
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Heat a medium to large Dutch oven or other heavy-bottomed pot over high heat. You're now going to brown the beef. Depending on how large your pot is, add half or all of the remaining oil. When the oil is hot, add the beef. Do not overcrowd the beef or it will not sear. Work in batches if you have to. Brown the beef on all sides and then transfer to a plate.
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Decrease the heat to medium and add the onion for about 10 minutes until it is nicely caramelized. Add the garlic, and cook for 1 more minute. Then add the lemongrass, tomato paste, ginger, star anise, and whole Thai chilis and cook for a minute or two.
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Add the beef and pour in the stock. Turn the heat back up to high and bring the liquid to a boil. Decrease heat so that the liquid is at a gentle boil, and simmer, covered, for 1 1/2 hours until the meat is tender.
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Add the carrots and daikon and cook for 30 minutes longer. Remove from heat and stir in fish sauce.
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Serve immediately and top with Thai basil or minced chilis if you want.