Hull and chop 6 ounces (170 grams) of the strawberries and place in a bowl. Mash using a potato masher, fork, or your hands to desired texture, then mix in the sugar. Transfer to a small pot and bring to a simmer over medium heat.
Simmer while stirring for 2-5 minutes to create a slightly thickened strawberry syrup. Remove from heat, cool to room temperature, transfer to a covered container, and refrigerate until chilled.
Once the syrup has cooled and is ready to assemble, hull and finely dice the remaining 4 ounces (113 grams) of the strawberries.
Divide the cooled strawberry syrup between two glasses. Top with the diced strawberries and pour in the milk.
Stir to combine the ingredients and serve immediately.