Combine sweetened condensed milk and coconut milk in the bowl of an electric mixer fitted with the whisk attachment. Whisk on high speed for 10 minutes, until smooth and has increased in volume a little. Add in the nut butter and whisk on high for 5 more minutes. Remove from stand. Cover the bowl with plastic wrap and refrigerator overnight.
Prepare ice cream according to your ice cream machine recommendations.
Remove from the ice cream churn and gently fold in the jam, taking care to leave streaks of jam. Pour into a lined 9x5 loaf pan. Eat immediately as soft serve or freeze overnight for scoops.