Combine strawberries and 2⅝ cups sugar in a medium saucepan.
Cook over medium/medium low heat, stirring as needed, to 226℉/108℃.
Remove from heat and allow to cool.
In a large bowl, combine milk, heavy cream, ⅓ cup sugar, vanilla, and salt.
Stir until sugar melts. Do not beat or whisk.
Pour into ice cream machine.
Freeze according to manufacturer's instructions.
Remove from machine and stir in strawberry jam.
Transfer to ice cream container and freeze 3-4 hours, or until firm.