Make the ice cream base according to the Classic Ice Cream Method, but add the mascarpone once the base has been made and it is still hot. Whisk thoroughly to completely dissolve the mascarpone.
Strain the base through a fine-mesh strainer and cool over an ice bath. Age the base under refrigeration overnight.
Once the base has aged, churn to the desired consistency.
Harden for at least 2 hours and up to 4 hours. Reserve until needed.