Add the blackberries to a bowl. Sprinkle 1/4 cup sugar over them and stir. Using a potato masher or wooden spoon, crush the berries to your desired size. I prefer mine mostly crushed with a few tiny chunks. Leaving the berries whole will not flavor the ice cream very well, and large berries will be hard to eat once frozen.
Pour the heavy cream into a large, separate bowl and set aside.
Add the whole milk and 1 cup sugar to a saucepan. Heat on medium low heat until steamy.
Place all the egg yolks into another separate bowl. Beat until pale yellow. Whisk in the heated milk mixture to temper the egg yolks. Then pour the egg yolk mixture back into the saucepan. Heat on low, whisking constantly, until the mixture thickens.
Pour the egg yolk mixture through a sieve into the bowl of heavy cream. Stir to combine. Add crushed blackberries and stir to combine.
Cover and chill your blackberry custard thoroughly in the fridge. Once it's chilled, then freeze it in an ice cream maker until thick. You can eat it immediately, or put it in a container in your freezer to harden.