In a medium saucepan, whisk together heavy cream, whole milk, half the brown sugar, cinnamon, ginger, nutmeg, and salt. Bring to a simmer over medium heat. In a separate bowl, whisk egg yolks and the remaining brown sugar until pale and thick.

Add the grated carrots to the warm cream mixture and simmer for 5-7 minutes until tender.

Slowly pour about 1 cup of the hot cream mixture into the egg yolks while whisking constantly to temper. Pour the tempered egg mixture back into the saucepan.

Cook the custard over low heat, stirring constantly, until it thickens enough to coat a spatula (approx. 170°F / 77°C). Do not boil.

Strain the custard through a fine-mesh sieve into a bowl set over an ice bath. Cool completely, then cover and chill in the refrigerator for at least 4 hours or overnight.

While the base chills, prepare the swirl: beat the softened cream cheese, powdered sugar, and vanilla extract in a small bowl until smooth. Set aside.

Churn the chilled custard in an ice cream maker according to manufacturer's directions. (For no-churn, see blog post notes).

In the last few minutes of churning, add the toasted pecans. Transfer half of the ice cream to a freezer-safe container. Dollop with half the cream cheese swirl and gently swirl with a knife. Repeat with remaining ice cream and swirl.

Cover and freeze for at least 4-6 hours, or until firm.