Beat 1/2 cup peanut butter, coconut sugar, coconut oil, and milk together in a bowl until smooth; cover and place in refrigerator.
Melt chocolate chips in top of a double boiler over simmering water, stirring frequently and scraping down the sides with a rubber spatula to avoid scorching; stir in butter until smooth. Set chocolate mixture aside to cool to room temperature, about 10 minutes.
Stir chocolate mixture into peanut butter mixture; cover and place in refrigerator.
Beat remaining 1 cup peanut butter and white sugar together with an electric mixer until smooth; beat in cream until well combined. Stir vanilla extract into cream mixture; cover and refrigerate for 3 hours or up to overnight.
Place cream mixture into the bowl of an ice cream maker; churn until soft-set and creamy, about 15 minutes. Chop chocolate mixture into pieces; mix about 1 cup chocolate mixture into ice cream.
Sprinkle remaining pieces of chocolate mixture over ice cream to serve.