In a small saucepan, combine the finely grated carrots, brown sugar, and spices. Cook over medium heat for 5-7 minutes, stirring, until carrots soften and a glaze forms. Cool completely.

Warm heavy cream and milk in a saucepan. In a separate bowl, whisk egg yolks and granulated sugar until pale. Slowly temper the egg yolks by whisking in about a cup of the hot milk, then pour the mixture back into the saucepan.

Cook the custard over low-medium heat, stirring constantly, until it thickens enough to coat the back of a spoon (6-8 minutes). Do not boil. Strain through a fine-mesh sieve, then stir in the vanilla and cooled carrot mixture. Chill for at least 4 hours or overnight.

In a small bowl, beat the softened cream cheese and powdered sugar together until completely smooth. Set aside in the refrigerator.

Pour the chilled base into your ice cream maker and churn for 20-25 minutes, or according to manufacturer’s instructions, until it reaches a soft-serve consistency. Add toasted nuts (if using) during the last few minutes of churning.

Spread half of the ice cream into a freezer-safe container. Dollop half of the cream cheese swirl on top and gently swirl with a knife. Repeat with the remaining ice cream and swirl. Cover tightly and freeze for at least 6 hours, or until firm.