01 - Combine diced strawberries, sugar, and lemon juice in a small saucepan. Cook over medium heat for 5-7 minutes, stirring occasionally, until strawberries are soft and syrupy. Mash lightly with a fork to break down larger pieces. Remove from heat and allow to cool completely.
02 - Distribute the cooled strawberry sauce evenly between two tall glasses. Add a few sliced fresh strawberries to each glass for added texture and presentation.
03 - Pour cold milk slowly over the strawberry sauce in each glass. Add ice cubes if desired. Gently stir with a spoon to create a swirled effect, mixing the sauce and milk partially while maintaining some visual separation.
04 - Serve the strawberry milk right away while chilled. The drink is best enjoyed fresh before the sauce settles completely at the bottom.