Combine milk, egg yolk, and light brown sugar in a small saucepan.

Cook over medium heat for 12 minutes, stirring constantly, until the mixture reaches 160°F.

Add butterscotch chips and vanilla extract, stirring until smooth.

Cover and refrigerate until completely cool.

In a large bowl, use an electric mixer to beat heavy cream until soft peaks form.

Add powdered sugar and vanilla extract.

Continue to beat until stiff peaks form.

Gently stir the cooled butterscotch mixture into the whipped cream until well combined.

Transfer the mixture to a freezer-safe container.

Freeze for at least 6 hours, or until solid.