Process strawberries and sugar in a blender or food processor until smooth, stopping to scrape down sides as needed. Press mixture through a wire-mesh strainer into a medium bowl, using back of a spoon to squeeze out juice; discard pulp. Stir in vanilla and salt. Stir strawberry mixture into cold milk. Chill 1 hour before serving. Refrigerate up to 3 days.
Spiked Strawberry Milk: Stir in 1/4 cup strawberry liqueur (such as De Kuyper Wild Strawberry) just before serving.