In a pot, combine blueberries, sugar, and water. Bring to a gentle boil, stirring occasionally, and let it simmer until the berries burst and release their juices.

For a smooth pudding, use a stick blender to puree the mixture. If you like it with texture, you can leave the berries whole.

Mix the cornstarch with a little cold water to make a smooth slurry. Slowly pour it into the simmering blueberry mixture, stirring constantly to prevent lumps.

Keep stirring and cook until the pudding thickens.

Remove from heat and stir in the vanilla. Let it cool slightly before serving.

Enjoy warm or chilled with a swirl of cream or a dollop of whipped cream!