Combine cream and half and half in saucepan and bring to a simmer. Whisk sugar, corn syrup and yolks together. Gradually whisk hot cream into yolk mixture. Return mixture to saucepan and heat until custard coats a spoon, about 10 minutes. (Do not boil.) Add cream cheese and stir until melted. Set aside.
Puree strawberries in a blender. (If desired, cut a few into small chunks.) Add strawberries, almond and vanilla extracts to custard and blend thoroughly. Refrigerate until chilled.
Fill an ice cream maker with the custard and freeze according to the manufacturer's directions.