In a small bowl, whisk 2 tablespoons of the milk with the cornstarch. Set aside.
In a large bowl, whisk the cream cheese until smooth.
In a large pot, add the rest of the milk, the heavy cream, sugar and salt. Cook on medium-low until the sugar dissolves.
Add the cornstarch/milk mixture to the pot and whisk to combine. Cook on medium until it thickens slightly.
Whisk the hot mixture into the bowl with the cream cheese until smooth.
Add the vanilla and whisk to combine. If you see little lumps in your mixture, sieve it before pouring it into an airtight container. Chill the base for at least six hours.
Churn the base according to your ice cream maker's instructions.
As you add the base to your ice cream container, stir in cake bits, cookie dough bites and additional sprinkles if desired.