Make the ice cream base according to the Modern Ice Cream Method. Add the almond paste (broken up in pieces) while the ice cream base is still hot. Whisk thoroughly to completely incorporate the almond paste solubles.
Strain the base through a fine-mesh strainer and cool the base 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.