Put the oats in the blender pitcher and add enough water to cover. Allow to soak for 15 minutes.
Add the blueberries to the oats and process until smooth.
Add the yogurt and ice. Process again until smooth.
Add a tablespoonful of brown sugar. Pulse a few times. Taste. Add more sugar, if the smoothie tastes too tangy. Pulse a few more times.
Pour the smoothie into glasses and serve at once.