Yield: 10 doughnuts
In a large bowl, whisk together flour, baking powder, salt, nutmeg, and cinnamon. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, cream together sugar, vegetable shortening, egg, and egg yolk. Scrape down bowl as needed to ensure thorough mixing.
Add vanilla, sour cream, and sweet potato puree. Mix on medium speed until well combined.
Add flour mixture in three additions. Mix on low speed until there are no longer any dry streaks of flour. The dough will be tacky and sticky. Use a sturdy spatula or a bowl scraper to transfer dough to a medium bowl. Cover with plastic wrap and let dough chill in the fridge for at least 1 hour (or up to overnight).
Attach candy thermometer to a large heavy bottomed pot (cast-ion or Dutch oven, preferred). Fill pot about 3-inches deep with shortening or oil. Set over medium heat to 350 degrees F.
Remove chilled dough from fridge. Dough will still be sticky. Transfer dough to a generously floured work surface. Flour the top the of the dough and pat (or roll) dough to a thickness of 1/2-inch. Using a floured 3 1/2-inch doughnut cutter (or round cookie cutters), stamp out doughnut rings. Transfer doughnut rings to lightly floured baking sheet.
Gather dough scrapes, knead together, and re-roll to stamp out more doughnuts.
Brush off any excess flour from the doughnut rings. Once oil comes to temperature, carefully place 2-4 doughnuts at a time into hot oil. Do not overcrowd the pot. Cook for 2 minutes on each side, until golden in color.
Drain cooked doughnuts on a wire rack over a paper towel lined baking sheet. Keep an eye on thermometer and adjust heat accordingly to maintain a constant cooking temperature.
Sift confectioners sugar into a large bowl. Stir in salt, corn syrup, vanilla, maple extract, and maple syrup. Once mixture is well combined, add in hot water. Mix until smooth.
Dip warm doughnuts into glaze. Allow excess glaze to drip back into bowl. Set glazed doughnuts on wire rack and allow glaze to set. Enjoy doughnuts warm or at room temperature.
A word on leftovers: Doughnuts are best enjoyed the day they are fried. Store any leftover doughnuts in a breathable box (like a cardboard bakery box or container with the lid slightly jar). The maple glaze needs air circulation, otherwise it will melt and make the cake doughnuts soggy.