In a saucepan over medium heat, combine blackberries, sugar, and lemon juice. Cook until the blackberries break down and release their juices, about 8-10 minutes.
Stir in the cornstarch slurry and cook for another 1-2 minutes until the mixture thickens. Remove from heat and let it cool completely.
For a smoother filling, mash the blackberries with a fork or blend the compote once cooled.
Notes
Store in an airtight container in the fridge for up to a week.