Add the milk and sugar to a medium-sized saucepan and cook over medium heat, stirring regularly, until the sugar is dissolved. Set aside to cool.
Add the strawberry puree to a medium sized saucepan over medium heat and cook until reduced by half, to about 1 cup. The mixture may come to a light boil, but you don’t really want it to start boiling a lot. Remove the strawberry mixture from the heat and add 3/4 cup of the milk mixture and stir to combine. Add the vanilla extract to the remaining milk and stir to combine. Set aside.
Add a couple slices of strawberries to each ice lolly mould, pressing them against the insides of the mould. Add some of the strawberry mixture to the bottom of the ice lolly moulds, so they are about 1/3 full. Freeze for about 1 hour.
Crumble 3-4 shortbread highlanders and add to the milk mixture. You want to be sure that the crumbled shortbread is in small enough pieces that they can fit into the ice lolly moulds. Divide the milk mixture among the ice lolly moulds so that each mould is now about 2/3 full.
Place an ice lolly stick into each lolly, making sure the stick goes down into the bottom strawberry layer at least about half way. This will be important for when you remove the lollies from the mould later. Freeze the ice lollies for about another hour.
Divide the remaining strawberry mixture among the ice lollies, then sprinkle some crumbled shortbread on top. Freeze until firm, 4-6 hours or overnight.
To remove the ice lollies from the mould, put the mould in room temperature water for several seconds and then wiggle free. Enjoy immediately or store in the freezer in a sandwich bag. We suggest wrapping the ice lolly in some parchment paper so they don’t stick to the bag.