Chop the strawberries roughly and put them in a small saucepan with the sugar and lemon juice. Let them sit for 5 minutes — they'll start releasing juice on their own.

Set the pan over medium-low heat. Cook, mashing the berries lightly with a fork as they soften, until the mixture turns into a loose, jammy syrup, about 4 to 5 minutes. It should still have some texture, not be fully smooth.

Take it off the heat and let it cool to room temperature, then refrigerate for at least 20 minutes. It needs to be genuinely cold or it'll melt your ice and water down the milk layer.

Divide the cooled strawberry mixture between two tall glasses, about 3 tbsp each, keeping it at the bottom.

Fill each glass most of the way with ice.

Pour the cold milk slowly over the ice, aiming at the ice rather than the strawberry layer, so it settles on top instead of mixing straight through.

Garnish with a strawberry slice on the rim and serve with a long spoon so whoever's drinking it can stir the layers together themselves.