Combine the strawberries and 1/3 cup sugar in a bowl; mash together with a potato masher. Store the mixture in the refrigerator while preparing the rest of the recipe.
Stir together the egg yolks, milk, salt and 1/3 cup sugar in a saucepan over medium heat. Heat to 175 degrees F (80 degrees C), making sure the mixture does not boil; transfer to a chilled bowl and move to the refrigerator to cool, stirring occasionally. Once cooled, stir in the cream, rosewater, and strawberry mixture.
Fill an ice cream maker with the mixture, and freeze according to the manufacturer's instructions.