Preheat oven to 350° F. In a medium bowl, combine graham cracker crumbs and melted butter. Stir until all crumbs are coated in the butter. Transfer to a 9" pie plate, and press the crumbs into the bottom and up the sides.
Bake crust until just golden, about 10 minutes. Cool completely.
For Purée:
In a small saucepan, combine blackberries, lime juice, and sugar. Stir to combine. Cook over medium heat until berries are soft and liquid is released. Transfer mixture to the bowl of a food processor.
Pulse berry mixture in the food processor until smooth. Strain using a fine-mesh strainer. You should end up with about ¾ cup juice. Set aside to cool completely.
For Filling:
In a large bowl, combine sweetened condensed milk and blackberry purée. Set aside.
In the bowl of a stand mixer, use the whisk attachment to whip the cream to stiff peaks. Fold the whipped cream into the blackberry mixture in three additions, working gently so as not to deflate the whipped cream.
Pour filling into cooled crust and smooth the top. Freeze at least 4 hours.
For Whipped Cream:
Place cold heavy cream, powdered sugar, and vanilla bean paste (see note) in the bowl of a stand mixer fitted with the whisk attachment. Start the mixer on low speed, and gradually increase the speed to high. Whip until the cream thickens and forms peaks.
Assembly:
Top the pie with the whipped cream and fresh berries. Pull the pie from the freezer about 30 minutes before you want to serve it.Enjoy!
Notes
Note on vanilla bean paste: You can substitute with vanilla extract if you like. I always have vanilla bean paste on-hand because it's my faaaaaave. If you're looking to purchase vanilla bean paste and can't find it in your local grocery store (I never can), you can find it online [here].