Insert wooden stick into each banana piece. Arrange on parchment-lined sheet pan and freeze for 20 minutes.
Place chips and morsels into separate bowls. Microwave on medium heat until melted, about 60 seconds, stirring every 30 seconds.
Remove bananas from freezer and dip by alternating between melted chocolate and butterscotch. Immediately roll them in chopped nuts or sprinkles. Freeze until frozen solid, about 1 hour.