Add the fresh blackberries, castor sugar, lemon juice, and zest in a small saucepan set over medium-high heat. Allow the fruit to soften and the sugar to melt.
As the compote cooks, the berries will release their water content, which will evaporate, and the filling will thicken. Make sure the mixture is not catching at the bottom of the pan. Stir occasionally with a spatula and press the fruit against the sides of the saucepan to help it break down a little, if needed.
Once the compote has thickened, remove the filling from the stovetop and pour it into a glass jar. Allow it to cool to room temperature.
Once cooled, you can add the compote as a filling or sauce for cakes and cupcakes. Enjoy!
Notes
If you'd prefer a smooth sauce rather than a chunky compote, you can use a fine mesh sieve to remove the seeds after the compote is done cooking and cooling.