Set the frozen orange juice concentrate on the counter to partially thaw, about 5 minutes. While it softens, place four serving glasses in the freezer to chill.

Add the partially thawed concentrate to a high-powered blender along with the ice, milk, water, sugar, and vanilla extract.

Blend on low speed for about 5 seconds to break up the ice, then increase the speed to high and blend for about 1 minute, until smooth. The texture should be thinner than a milkshake — more like a frothy, slightly icy smoothie.

Pour immediately into the chilled glasses and serve right away, while it's still frosty and thick.