Preheat oven to 425° F. Line a large baking sheet with parchment paper. Set aside.
Whisk together heavy whipping cream, orange juice and lime juice in a medium bowl; until soft peaks form. Set aside.
Melt butter in a medium saucepan over medium heat. Stir in sugar and water until a thin syrup forms. Turn heat off. Add carrots and stir, coating evenly with syrup.
Transfer carrots to baking sheet, drizzle with remaining syrup. Bake for 20 minutes. Remove from heat and set aside to cool.
Place carrots and milk in a blender. Blend until smooth.
Add lime zest, orange zest, maple syrup, vanilla, cinnamon, nutmeg and salt to whipping cream and juice mixture. Stir to mix well. Add carrot mixture and whisk until evenly combined. Cover and refrigerate for 1 hour.
Place mixture in ice cream maker. Churn for 25 minutes, adding dulce de leche in the last 3 minutes of churning.
Scoop ice cream into serving bowls, drizzle with dulce de leche and a sprinkle of pecans.