Peel and stone avocados and cut flesh into 2cm dice. Toss in lemon juice to prevent browning. Place pieces into a snap lock bag and freeze for 4 hours or until firm.
Meanwhile, combine sugar and cup water in a saucepan and bring to a simmer over medium heat. Remove from heat, stir in cocoa and vanilla and set aside to cool completely. Chill for 30 minutes until thickened.
Remove avocado from the freezer and stand for 5 minutes. Transfer avocado to the bowl of a food processor with a pinch of salt. Process until very finely chopped, scraping down the sides of the bowl if needed. Gradually add cocoa mixture and milk and process until smooth.
Transfer to a 1L freezer-safe container and freeze for at least 4 hours. Remove from the freezer 5-10 minutes before serving. Using a hot spoon, scoop ice-cream into ice-cream cones, drizzle with melted chocolate and scatter with chopped hazelnuts.