Place strawberries and sugar in a blender and pulse until pureed; steep for 10 minutes.
Pour cream, milk, vanilla extract, and salt into strawberry mixture; blend until smooth and slightly thickened, 10 to 15 seconds. Whisk red food color into cream mixture.
Pour strawberry mixture into the container of an ice cream maker and freeze according to the manufacturer's instructions. Transfer ice cream to a sealable container, cover the ice cream with plastic wrap, seal the container, and freeze, 2 hours to overnight.
Process in an ice cream maker until thick. Immediately transfer to a sealable container, cover with plastic wrap, cover the bowl with a lid and freeze for 2 hours to overnight.