Whisk together eggs, sugar, and salt in a bowl, then add hot milk in a slow stream, whisking.
Pour custard back into saucepan and cook over moderately low heat, stirring with a wooden spoon, approx 2 to 3 minutes, the custard will coat the back of the spoon.
Immediately pour custard through a fine-mesh sieve into a clean bowl.
On very low speed, blend in cream cheese until thoroughly incorporated.
Stir in cream and vanilla.
Place plastic wrap directly onto surface of custard mixture and refrigerate for at least 4 hours or over night.
Freeze completely cooled custard in ice cream maker.
When custard is nearly done, add sliced strawberries.
Complete freezing process and transfer to an airtight container.
Place in the freezer to cure for about two hours.
Allow to stand at room temperature 5-10 minutes before serving.