For the strawberry sauce in a small saucepan combine the chopped strawberries, 60gr sugar and the lemon juice, cook on medium until sugar dissolves and the syrup thickens about 5min. Cool. Transfer into a blender and blend until smooth. Run the sauce through a sieve and leave until ready to use.
Dissolve the cornstarch in 50ml whole milk, leave to rest.
For the ice cream base in a small saucepan over medium heat combine the heavy cream, the leftover whole milk, 60gr sugar, pinch salt, stir, being to an almost boil, add the cornstarch milk and cook constantly stirring until thickened. Take off heat, add the cream cheese and the strawberry sauce, mix until smooth. Transfer into the fridge overnight.
Freeze in your ice cream maker according to the manufacturer's instructions. Store in an airtight container swirling in pockets of strawberry jam (5-6tsp) and place in the freezer until set.