Process rice in the jar of a blender until fine crumbs form. Transfer to a medium bowl. Add the water, and stir to combine. Cover with plastic wrap, and place in refrigerator 3 hours or overnight.
Transfer rice and soaking liquid to the jar of a blender; add desired fruit, vanilla, cinnamon, and evaporated milk, if using. Blend on high speed until smooth, about 1 minute; sweeten with honey, if desired. Strain through a sieve into a medium bowl; discard solids. Serve over ice.