Combine the beef stock, lime juice, fish sauce and sugar in a large saucepan. Bring to a simmer over a medium heat, whisking occasionally until the sugar has dissolved.
Add the chilli, celery and ginger, stir well, and simmer for a few more minutes. Add beef and noodles to the saucepan and simmer for 8-10 minutes until the noodles are soft and the beef is cooked. Season to taste with pepper, then stir through the chopped basil. Ladle into serving bowls and serve immediately.
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