Warm a large pan over a medium heat. Add a couple tablespoons of water and sauté the onions until translucent ( you can use oil 1 tablespoon of oil rather than water if you prefer).
Add the garlic and curry powder and cook for a couple of minutes, stirring frequently.
Add the arrowroot and stir well to distribute then gradually add the water, stirring as you go to work out any lumps.
Pour in the potatoes, cover with a lid and allow them to cook through, giving it a quick stir every 5 minutes or so. You can check the potatoes by piercing them with a fork.
When the potatoes are tender (it will take around 15 minutes) remove from the heat, add the green beans then add the coconut milk. Do it in that order to avoid curdling issues. The green beans will lower the heat of what's in the pan before you add the coconut milk.
Add the sugar and stir really well.
Return to a medium/low heat and allow everything to warm through again and the beans to cook (about 7-10 minutes). Some bite left in the beans is good and remember that they will continue cooking a little while you are plating up.
Season with salt and pepper to taste and as soon as the beans are tender it is ready to serve.
If you like bit of heat in your curry feel free to add some chili flakes or a fresh chopped chili just before you add the water to the pan. Leftovers reheat well and will keep in the fridge for up to 4 days.