Place bananas in a food processor; puree until smooth.
Stir sweetened condensed milk with pudding mix in a large bowl. Stir in banana puree, whole milk, heavy whipping cream, and light whipping cream until smooth. Chill pudding mixture in freezer for 1 hour, scraping down sides and stir after 30 minutes.
Pour the chilled mixture into an ice cream maker and freeze according to manufacturer's directions until it reaches "soft-serve" consistency. Gently stir in almonds. Transfer ice cream to a one- or two-quart lidded plastic container; cover surface with plastic wrap and seal. For best results, ice cream should ripen in the freezer for at least 2 hours or overnight.