In a medium sauce pan, heat strawberries, sugar, 2 tablespoons water, and vinegar. Bring to a simmer, reduce heat to low (but still simmering), cover, and cook for 15 minutes.
In a small bowl, mix remaining water and cornstarch. Whisk into the strawberry mixture after it has cooked 15 minutes and cook for about 1 more minute until thickened. Remove from heat and puree until smooth with hand blender or in a standing blender.