In blender container, blend blackberries and water until smooth. Add lime juice and stir.

In small saucepan, heat honey and serrano pepper slices on medium. Simmer for 10 minutes. Add blackberry purée and continue to cook on low simmer for further 10 minutes; allow to cool. Add pinch of salt.

Press purée through sieve to remove seeds. Chill purée thoroughly, about 1 hour.

Place purée in bowl of ice cream maker and churn until desired consistency is reached, about 20 to 30 minutes, depending on your maker. Place in freezer-proof container and freeze for 1 to 2 hours to firm up further.