Use a blender to purée the 1 ¼ cups (180 g) strawberries that we need to make the strawberry syrup.
Add the purée, sugar, and half the diced strawberries into a small saucepan and bring it to a boil. Continue to cook for 2 more minutes on medium-low, stirring occasionally.
Cool the strawberry syrup completely in the refrigerator. (If you don't completely cool the strawberry syrup before combining it with milk, you may cause the milk to curdle.)
Split the cooled syrup between 2 glasses (this recipe makes 2 servings). Use a spoon to swirl the syrup around in the glass to get some on the inner sides.
Pour in the milk. Top with whipped cream, if desired. Then split the remaining diced strawberry pieces between the glasses.
