These homemade fried sour cream donuts are dipped in brown butter glaze.
In a large bowl, whisk together cake flour, baking powder, salt, nutmeg, and cinnamon. Set aside.
In the bowl of stand mixer fitted with a paddle attachment (or using an electric hand mixer), cream together sugar, vegetable shortening, egg, and egg yolk. Scrape down bowl as needed to ensure thorough mixing.
Add sour cream. Mix on medium speed until well combined.
Add flour mixture in three additions. Mix on low speed until there are no longer dry streaks of flour. The dough will be VERY tacky and sticky. Use a sturdy spatula or bowl scraper to transfer dough to a medium bowl. Directly cover dough with plastic wrap. Chill dough in the fridge for at least 1 hour, or up to overnight.
Attach candy thermometer to a large heavy bottomed pot (cast iron or Dutch oven, preferred because of heat retention). Fill pot about 3-inches deep with shortening or oil. Set over medium heat and bring to 350 degrees F.
Remove chilled dough from fridge. Dough will still be VERY sticky. Transfer dough to a generously floured work surface. Flour the top of dough and pat (or roll) dough to a thickness a little under 1/2-inch.
Using a floured 3 1/2-inch doughnut cutter (or using round cookie cutters), stamp out doughnut rings. Transfer rings to a lightly floured baking sheet.
Gather dough scrapes, knead together, and re-roll to stamp out additional doughnut rings.
Brush off any excess flour from doughnut rings. Once oil comes to temperature, carefully place 2-4 donuts at a time into hot oil. Do not overcrowd the pot. Cook for 90 seconds to 2 minutes on each side, until golden in color.
NOTE: Keep any eye on thermometer and adjust heat accordingly to maintain even, constant cooking temperature.*
Drain cooked doughnuts on a wire rack or paper-towel lined baking sheet.
In a heavy bottomed sauce pot, melt butter over medium heat. Once the butter has melted, continue to cook. Swirl pan occasionally to ensure even heating. The mixture will bubble and foam as it cooks. The bubbling will be vigorous at the beginning, but it will subside.
Continue to cook until butter smells nutty and the milk solids at the bottom of the pot have turned rich golden brown in color.
Remove from heat and pour into a heat-safe bowl. Be sure to scrape out as much from the browned milk solid bits. Set aside.
Sift powdered sugar into a medium bowl. Stir in corn syrup, vanilla, and warm brown butter. Once mixture is well combined. add in hot water. Mix until smooth.
Dip warm donuts into glaze. Allow excess glaze to drip back into bowl. Set glazed donuts on wire rack. Allow glaze to set. Enjoy donuts immediately, warm or at room temperature.
Storage and Leftovers: Donuts are best enjoyed the day they are fried. Store any leftover donuts in a breathable box (like a cardboard bakery box or container with the lid slightly ajar). The glaze needs air circulation, otherwise, it will melt and make the donuts soggy.