Meanwhile, in food processor or blender, place 1 cup of the strawberries. Cover; process until smooth. Pour pureed berries into 1-quart saucepan. Stir in sugar and cornstarch. Bring strawberry mixture to boiling, over medium-high heat, stirring constantly. Reduce heat to low; cook, stirring one additional minute. Remove from the heat; let it stand 20 to 30 minutes to cool, stirring once or twice.