Make the carrot puree:
In a medium saucepan, combine the carrot slices whole milk, ground cinnamon, ginger, cloves, nutmeg, orange peel, and brown sugar. Bring to a boil over medium heat, and then reduce the heat to low and simmer until the carrots are tender.
Transfer the carrot mixture to a blender and blend on high until smooth. Scoop out every bit of the puree, transfer to small a bowl and set aside. You should have about 1 1/3 cups of carrot puree.
Make the ice cream base:
To a medium saucepan, add the carrot puree, whole milk, heavy cream, granulated sugar, brown sugar, salt, and condensed milk. Cook over medium heat and bring to a simmer. Once the mixture has simmered, turn off the heat. Taste and adjust the spices as needed. Cover and allow the mixture to steep for about an hour.
When the mixture has steeped long enough - Prepare a large bowl with ice water, a bowl large enough to hold a smaller bowl with your egg custard. Separate your egg yolks into the bowl. Add the steeped carrot base to the egg yolks, stirring until completely incorporated. Add the mixture to the saucepan and cook over medium/low heat, stirring THE ENTIRE TIME until the mixture thickens and coats the back of a wooden spoon.
Pour the mixture in a bowl lined with the strainer, nestled in the ice water bowl and allow the mixture to cool completely, stirring every once in a while. Once the mixture has cooled, you can allow the mixture to steep overnight in the refrigerator or you can freeze right away. As your custard cools, make the cream cheese whipped topping.
Make the whipped cream cheese topping:
In a bowl fitted with a whisk attachment, add cream cheese, confectioners' sugar, vanilla bean paste and vanilla extract. Begin mixing over low speed until the confectioners' sugar is somewhat incorporated.
Increase the speed to high and whip until combined and mixture is smooth. Stop and scrape the mixer. Continue whipping on high and add the heavy cream in a slow stream, to allow the whip cream to thicken.
Whip until the mixture is thickened and smooth. Stop the mixer. Add the cheesecake mixture to a piping bag fitted with a star or round tip. A ziplock bag works here too. Be sure to snip the end of the ziplock bag. Place in the fridge until ready to use While the cheesecake chills, make the candied walnuts.
Make the candied walnuts:
In a medium skillet and the butter and melt slightly. Add the sugar and vanilla extract, followed by the walnuts. Cook over medium heat stirring the mixture frequently to ensure your walnuts do not burn. When the sugar begins to melt, stir quickly to make sure your walnuts are completely coated with the sugar mixture.
Transfer the walnuts to a sheet of parchment; allow the walnuts to cool for a few seconds and then separating the nuts. You can fold the parchment in half and have at it with a rolling pin, or you can do this with your hands. Once the nuts have cooled, transfer them to an airtight container until ready to use.
Assemble this bad boy:
Get an ice cream bowl. Big, small – Don’t matter. Scoop ice cream into your bowl; add a swirl, or small dollop of cream cheese whipped topping. Finally top this jammy with candied walnuts. Go in on that.