Hull and chop 6 ounces (170 grams) of the strawberries and place in a bowl. Mash using a potato masher, fork, or your hands until crushed, then mix in the sugar and optionally the lemon zest and lemon juice, if using.
Transfer the mixture to a small pot and bring to a simmer over medium low heat.
Simmer while stirring for 2-5 minutes until the mixture becomes a slightly thickened strawberry syrup.
Remove from heat, then stir in the vanilla extract, if using.
Allow the syrup to cool to room temperature, then transfer to an airtight container and refrigerate until chilled, about 1 hour.
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.