Spiced Carrot Baba Au Rhum with Candied Carrots and Pistachios

Name: Spiced Carrot Baba Au Rhum with Candied Carrots and Pistachios
Ingredients: 2 cups carrot juice; 1 (1-inch) piece fresh ginger, peeled and finely grated; 3 ounces (6 tablespoons) unsalted butter, softened; more for the molds; 1- 1/2 cups all-purpose flour; more for the molds; 1-1/2 teaspoons ground allspice (I didn't have this spice so I used apple pie spice); 1 teaspoon cinnamon; 1/2 teaspoon ground star anise (I didn't have this spice so I just omitted it); 1/2 teaspoon baking soda; 1/4 teaspoon salt; 1/4 cup packed light brown sugar; 2 large eggs; 1/4 cup chopped unsalted pistachios (for garnish); 2 cups granulated sugar; 2 large carrots, peeled and cut into long julienne strands to yield 1 cup; 1 cinnamon stick