In a large bowl, combine sweetened condensed milk and vanilla extract. Set aside.

Using a hand mixer or stand mixer, whip the heavy cream until stiff, billowy peaks form. Gently fold half the whipped cream into the condensed milk, then add the other half.

In a separate bowl, use a fork or potato masher to mash the blackberries and granulated sugar.

Pour half the ice cream base into a 2 quart container (I used a loaf pan). Top with half the smashed blackberries and use a knife to swirl the blackberries into the ice cream. Pour in the remaining half of the ice cream base and top with remaining smashed blackberries. Swirl the remaining blackberries into the ice cream.

Cover and freeze until firm, at least 6 hours.