In a medium bowl, stir condensed milk and vanilla. Set aside.
In a large bowl, pour whipping cream. Beat with an electric mixer until stiff peaks form.
Soften the milk mixture by adding a blob of whipped cream. Stir it in.
Gradually fold milk mixture into whipped cream. Keep folding until it's almost mixed but a few billows of whipped cream remain.
Starting with whipped cream mixture, alternate layers with blackberry crush. End with a few tablespoons of blackberry crush on the top. Gently swirl it in.
Place plastic wrap directly on the surface to prevent ice crystal formation.
Place in freezer for at least 6 hours or until firm.