Step 1

Add finely shredded carrots and whole milk to a blender. Process until completely smooth.

Step 2

Pour 1 cup heavy cream and vanilla into a large bowl, with a mesh strainer set on top. Set aside.

Step 3

Add contents of blender, remaining 1/2 cup heavy cream, sugar, cinnamon and salt to a small saucepan. Cook over medium heat, stirring to dissolve sugar.

Step 4

In a small bowl, whisk together egg yolks.

Step 5

When milk mixture begins to steam, remove 1 cup warm liquid and slowly drizzle into egg yolks while whisking continuously. Pour mixture back into small saucepan and continue to cook, stirring occasionally, until mixture coats the back of a wooden spoon or rubber spatula.

Step 6

Pour hot liquid through the mesh strainer into reserved heavy cream. Stir to combine. Cool over an ice bath to room temperature. Cover and chill thoroughly.

Step 7

Churn ice cream according to manufacturer's directions.

Step 8

Meanwhile, prepare frosting. In a medium bowl, beat together cream cheese and butter until smooth. Mix in vanilla and powdered sugar, followed by heavy cream. Transfer mixture to a piping bag or plastic storage bag with the end snipped off.

Step 9

Transfer ice cream to a freezer safe container, adding streaks of frosting throughout. Freeze until firm, 4-6 hours or overnight.