In a small saucepan, combine the finely grated carrots, brown sugar, cinnamon, nutmeg, ginger, and 2 tablespoons of water. Cook over medium heat for 5-7 minutes, stirring occasionally, until the carrots are tender and the mixture is fragrant. Remove from heat and let it cool completely.

In a medium saucepan, warm the heavy cream, whole milk, and granulated sugar over medium heat, stirring until the sugar dissolves. While the milk warms, whisk the egg yolks in a separate bowl.

Slowly pour about one cup of the warm milk mixture into the egg yolks, whisking constantly. Pour the tempered egg mixture back into the saucepan.

Cook over medium-low heat, stirring constantly, until the custard thickens enough to coat the back of a spoon (approx. 170°F or 77°C). Strain through a fine-mesh sieve into a clean bowl.

Stir the cooled carrot mixture and vanilla extract into the custard. Cover and refrigerate for at least 4 hours, or preferably overnight.

Beat the softened cream cheese and powdered sugar together until smooth and creamy.

Pour the chilled base into your ice cream maker and churn according to the manufacturer’s directions. Add the toasted pecans during the last few minutes of churning.

Layer the churned ice cream and spoonfuls of the cream cheese swirl in a freezer-safe container. Gently swirl with a knife. Cover and freeze for at least 6 hours, or until firm.