Prepare pastry crust by combining cold butter with flour, salt, sugar and ice water. Wrap in plastic and chill 30 minutes.
1 ½ cup all purpose flour, ½ cup butter, 2 teaspoons granulated sugar, ½ teaspoon salt, 4-6 tablespoons ice water
Preheat oven to 400 degrees Fahrenheit. Roll pastry out to about 12" round and transfer to a 9" pie dish. Place in preheated oven and bake until slightly puffy, 10-15 minutes. Remove and set aside. Reduce oven to 325 degrees.
1 9" pastry crust
Meanwhile, combine 4 tablespoons melted butter with ¼ cup brown sugar and toss carrots and sweet potatoes in the mixture to coat.
4 large carrots, ½ cup butter, ½ cup brown sugar, 1 small sweet potato
Place vegetables in a single layer on a baking sheet and roast until tender, 25-30 minutes turning halfway through. Remove and cool.
Meanwhile, melt the remaining 4 tablespoons butter in a small saucepan over medium heat. Add remaining brown sugar, ½ teaspoon salt, and ½ cup heavy cream then stir to combine. Bring to a boil then simmer 4 to 5 minutes or until thick. Remove from heat and cool.
1 ½ cups cream
Place roasted carrots and sweet potatoes in a blender or food processor. Add remaining 1 cup cream, spices, eggs and half the caramel sauce to blender with carrots and sweet potatoes. Blend until smooth and pour into prepared pie shell.
2 large eggs, 1 teaspoon salt, ½ teaspoon cinnamon, ¼ teaspoon ground ginger, ⅛ teaspoon nutmeg, ¼ teaspoon ground all spice, ⅛ teaspoon cardamom
Bake in the center of preheated oven until center is set, 45 to 60 minutes.
Remove from oven and allow to cool completely before cutting and serving with whipped cream and reserved caramel sauce.