In a saucepan over medium heat, cook the berries until liquid escapes and they are very soft.

Carefully transfer to a blender or food processor (don't seal the lid completely so the steam can escape) and blend until completely smooth.

Strain through a sieve to remove most or all of the seeds. Discard seeds and set aside berry puree.

In a saucepan or heavy-bottomed pot, combine cream and milk and cook over medium-low, stirring frequently, until it comes to a simmer (try not to let it boil). While the mixture heats, whisk together the egg yolks and sugar in a bowl (it will be very very thick).

When the milk mixture reaches a simmer, remove from heat and scoop out 1/3 cup of the mixture and pour in a slow stream, whisking constantly, into the egg/sugar mixture.

Return the milk mixture to the stovetop and turn the heat to medium-low. Whisking constantly, pour in the egg mixture and let cook until it thickens and coat the back of your spoon or spatula.

Remove from heat and stir in the berry puree, the cream cheese, and vanilla. Mix until cream cheese is completely combined.

Refrigerate until it's completely chilled, then freeze in an ice cream mixer according to manufacturer's directions.

Spoon into a covered container and let freeze for about 2 hours before serving (or you can serve it right away if you don't mind your ice cream a little soft and you have little mouths clamoring for a taste).