Blend the blackberries with 2 tablespoons of the honey until completely smooth.
Optional: Strain the berry puree through a fine-mesh sieve to remove seeds.
In a large bowl, whisk together the Greek yogurt, remaining honey, lemon juice, vanilla, and salt.
Gently stir or swirl the blackberry puree into the yogurt mixture until desired pattern is reached.
Pour the mixture into a shallow, freezer-safe container (like a 9x5 metal loaf pan).
Place in the freezer and stir the mixture with a fork every 45 minutes for the first 2 hours.
Smooth the top and allow to freeze undisturbed for another 2–3 hours or until firm.
Let the container sit at room temperature for 10 minutes before scooping for the best consistency.