Make the cake: Adjust the oven rack to the center position and preheat the oven to 350 degrees F (175 degrees C). Spray a standard 10-cup (2.5-liter) Bundt pan with cooking spray.
In a large bowl, stir together the flour, baking soda, baking powder, salt, and pumpkin pie spice. Set aside. In the bowl of a stand mixer, beat the oil and brown sugar on medium speed until light and fluffy. Add the eggs, one at a time, beating well after each egg and scraping down the sides of the bowl. Add the vanilla and sweet potatoes and blend on low until thoroughly mixed. Gradually add the flour mixture and beat on low speed until just incorporated.
Pour the batter into the prepared pan and smooth the surface. Bake for 1 hour 15 minutes to 1 hour 30 minutes, or until a toothpick inserted in the center comes out clean and the edges start to pull away from the sides of the pan. Let cool in the pan for 10 minutes, then invert onto a rack and cool completely.
Meanwhile, make the icing: In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese until smooth. Add the mascarpone, heavy cream, and sugar, then mix on low until uniform. Scrape down the sides if needed to ensure everything is getting mixed in. Add the vanilla bean seeds and the maple extract to the bowl. Mix to combine, then increase the speed and beat for 1 to 2 minutes, until the icing is nice and thick. Put the icing in an 18-inch (46-cm) pastry bag. Snip off the tip.
When the cake is cool to the touch, use a back-and-forth motion to drizzle the top of the cake with the icing from the center to the outside and back again. Repeat until the entire cake is iced.
Recipe from "Southern Girl Meets Vegetarian Boy." Copyright 2017 by Damaris Phillips. By arrangement with ABRAMS.