Begin the strawberry puree by washing and drying the fresh strawberries. Remove the stems and slice, then roughly chop.
Add to a skillet or saucepan over medium heat. Add the sugar, folding it into the chopped strawberries. Cook down until the consistency becomes syrupy, with softened chunks of strawberries remaining.
Remove from heat and transfer to a storage container. Seal, then place in the fridge to chill for at least two hours.
When ready to serve, use a spoon to scoop the strawberry puree into your glass. Use the back of the spoon to swirl the puree around the inside of the glass, then add ice cubes (if using). Pour the whole milk on top, and enjoy immediately.