In a small saucepan over medium-high heat, scald milk until bubbles form around the edges, but don’t boil.
Remove from heat, and stir in sugar and salt until dissolved.
Mix in vanilla, half & half, and whipping cream. Whisk in pureed banana.
Cover and refrigerate for 30 minutes. After, place in ice cream maker and follow manufacturer’s directions.
Before placing in freezer, pour contents into a container with a tight-fitting lid. Drizzle the cookie butter into the mixture while gently folding it in.
Place sealed container in the freezer until ice cream hardens.