Cook the Udon noodles in a saucepan of simmering salted water and keep aside until needed.
Preheat a saucepan over medium high heat.
Drizzle some oil and add the beef. Cook for 2 minutes until coloured. Add the chopped and sliced vegetables except the lime.
Stir fry for 2-3 minutes over high heat, stirring once or twice to ensure all the vegetables are stir-frying.
Add the curry paste and again toss to coat all the vegetables.
Add the tin of coconut milk and place a lid over the pan. Cook for a further 5 minutes until the vegetables starts to just soften.
Turn off the heat and add the Udon noodles. Stir to coat the noodles in the sauce and serve immediately with a squeeze of lime and a sprinkle of coriander leaves.