Place the rice in a bowl with enough water to cover it and let it soak overnight.
Strain the rice and discard the water. Place the drained rice into a liquidiser. Pour 125ml of the cold water and 450ml of evaporated milk into the liquidiser. Blend until the rice is finely ground, about 30 seconds. Add the sugar, cinnamon and vanilla; blend well. Pour in the remaining diluted evaporated milk and cold water; blend.
Line a sieve with two layers of cheesecloth. Place the sieve over another bowl to catch the liquid. Pour the rice milk through the cheesecloth, discard the solids. Repeat the process if necessary. Serve over ice.