In a medium saucepan, cook the blackberries, sugar, and water together over medium heat. Use a fork or potato masher to smash the berries as they cook. Once mixture begins to simmer, continue cooking and stirring for 5 minutes.
Pour mixture through a fine mesh sieve, using a rubber spatula to push as much juice from the berry solids as possible. You should end up with about 2/3 - 3/4 cup berry juice. Transfer berry juice to a glass measuring cup and chill in the refrigerator until cooled completely.
In the chilled bowl of a stand mixer fitted with the whisk attachment, whip the heavy cream until stiff peaks form.
Pour sweetened condensed milk and vanilla into a large mixing bowl. Gently fold a third of the whipped cream into the condensed milk until combined. Add the rest, and continue folding until you see just a few streaks of white.
Remove half of the mixture, scooping it into another bowl. To this half of the mixture, fold in the cooled berry juice until just combined.
Drop a few spoonfuls of the berry custard and vanilla custard into a freezer-safe container. Sprinkle with the cooled streusel crumble. Repeat this layering process until you've used up both custards and all of the streusel crumble. Using a skewer or butter knife, swirl figure-eights throughout the ice cream.
Chill the ice cream in the freezer for at least 6 hours, preferably overnight.
Scoop, serve, and enjoy!