In a blender or food processor, blend the fresh blackberries until smooth.
Add the blackberries and brown sugar to a pot and cook on medium heat for 10-15 minutes. Let cool completely.
In a large mixing bowl, beat the heavy whipping cream until soft peaks form.
In a separate bowl, whisk the mascarpone cheese, vanilla, and sweetened condensed milk until smooth. Gently fold the mascarpone into the whipped cream until fully combined.
Add the blackberry puree and gently fold everything together.
Transfer the mixture into a loaf pan or a freezer-safe container.
Smooth out the top and cover with plastic wrap, ensuring it touches the surface of the ice cream to prevent ice crystals from forming.
Place the pan in the freezer and let it chill for at least 6 hours, or until firm.