Add the carrots to a saucepan and cover with just enough salted water. Boil until fork tender, then drain and immediately mash or blend until smooth while still hot.
While the mashed carrot is still warm, mix in 200g of the glutinous rice flour until a dough forms. Add more flour as needed until the dough is smooth and no longer sticky – if your dough is too crumbly add some hot water to bring it together.
Pinch off small pieces of dough, roll into balls, then press your finger into the centre to create a little button shape. Cook the button noodles in boiling water for about 3 minutes (or a good rule of thumb is to take them out 30 seconds after they float to the surface).
Divide the noodles across two bowls then top with garlic, spring onions and chili flakes. Pour over the hot oil, then stir in the soy sauce and vinegar. Stir through the button noodles and serve immediately.
