Combine strawberries, sugar, 2 tablespoons water, and balsamic vinegar in a saucepan; bring to a simmer over medium heat.
Reduce heat to medium-low, cover, and simmer for 15 minutes.
Whisk 2 tablespoons water and cornstarch together in a small bowl.
Whisk cornstarch mixture into strawberry mixture. Cook, stirring constantly, until mixture thickens, 1 to 2 minutes. Remove from heat.
Transfer mixture to a blender and puree until smooth.
Chef John serves this sauce over his New York-Style Cheesecake.