Set aside 3/4 cup (100g) of blackberries. Combine the remaining 1 cup (140g) of blackberries with the granulated sugar, lemon juice and cornstarch in a small saucepan. Bring to a boil, over medium heat. Boil for 1 minute. Turn the heat down to low and simmer, stirring occasionally, until the blackberries soften and break down, about 6-8 minutes. Smash the blackberries with the back of a spoon as they cook. Pass the blackberries through a sieve or a food mill to remove the seeds. Stir in the reserved blackberries and set aside to cool to room temperature.