Position a rack in the lower third of the oven and preheat to 400°. In a large saucepan, cook the strawberries, sugar, cornstarch, lemon juice and vinegar over medium heat, stirring, until syrupy, about 7 minutes. Lower the heat and simmer, stirring, until reduced to about 1-1/4 cups, 10 to 15 minutes; let cool.