Place a large glass or metal pan inside another larger bowl filled with ice. Add the heavy whipping cream to the bowl set inside the ice bath. Place a fine mesh strainer over the cream. Set aside.
In a medium mixing bowl, combine ¼ cup (57g) of the sugar and the egg yolks. Whisk until the egg mixture is pale and slightly thickened. Set aside.
Pour the milk into a heavy bottomed, medium saucepan. Add the remaining ½ cup (113g) of sugar and the salt. Warm over medium heat, stirring constantly, until the mixture just comes to a boil. Remove from the heat.
Temper the eggs by slowly drizzling a little hot milk into the eggs while whisking constantly. After more than half the hot milk has been added to the eggs, pour the egg/milk mixture back into the saucepan whisking to combine. Cook over medium heat stirring constantly until the custard coats the back of a wooden spoon.
Remove from the heat and add the cream cheese. Emulsify with an immersion / stick blender until smooth (if desired) or smash with a spatula to combine. Pour the base mixture through the sieve into the bowl with the heavy cream set over the ice bath. Discard any clumps left in the strainer. Stir occasionally while cooling, about 30 minutes.
Once cooled, add the vanilla extract and stir until well blended. Cover and refrigerate the mixture for at least 8 hours or overnight.
Process the custard according to the directions for your ice cream maker. Serve immediately as soft serve ice cream or freeze in an airtight container for several hours or overnight for a firm, scoopable consistency.