Toss the frozen strawberries with the sugar and let them stand for 5 minutes until their surfaces look glossy.

Chill two tall glasses in the freezer while the berries stand.

Add the milk, lemon juice, strawberries and ice cream to a blender in that order.

Pulse 6 times, then blend for 20 seconds until pale pink with tiny berry flecks and no hard fruit pieces.

Pour into the cold glasses and serve immediately.