Mix strawberries, sugar and salt in a heavy saucepan. Let stand 10 minutes off heat. Mash mixture with potato masher until all berries have broken up. Puree one-half strawberry mixture in a blender, then return to the saucepan. Heat mixture gently only until fragrant, about 5 minutes. (Be careful to not overcook.) Stir in heavy cream, milk and vanilla and chill in refrigerator overnight.

Pour mixture into an ice cream maker and freeze according to manufacturer's directions.

Note
For a smoother ice cream, puree strawberry mixture before heating it.