In a 2-quart saucepan, add strawberries, sugar and water. Bring to a boil over medium heat, stirring constantly. Reduce heat and simmer for about 2 minutes to soften strawberries and dissolve sugar. Set aside to cool. Mash cooled ingredients with potato masher or wooden spoon.
In a separate bowl, whisk together milk, cornstarch and vanilla. Slowly whisk milk mixture into cooled berries,
Return saucepan to the stove. Heat over medium-low heat, whisking constantly until pudding starts to thicken, about 2 minutes. Simmer an additional minute on low heat. Pour finished mixture into 3 individual bowls, approximately 1/2 cup each. Chill until set.