Start by preparing the dough. In a large bowl, whisk together the cake flour, baking powder, salt, nutmeg, and baking soda. Set aside.
In a separate large bowl, whisk together both sugars and the melted butter. Add the eggs, egg yolk, and vanilla, and whisk until well combined. Then, whisk in the buttermilk.
Add the dry ingredients to the wet, and fold to mix until just combined (the dough will be very sticky). Cover the bowl and place in the fridge to chill for at least 30-60 minutes.
Once chilled, heavily flour a work surface and your hands. Lay the dough onto your work surface, sprinkle the top with more flour, and gently roll/pat it down into a large rectangle (18x3.5”; ½” thick), adding more flour as needed (the dough is very soft, so don’t be afraid to use extra flour).
Flour a bench scraper or knife, and cut the dough all the way across lengthwise to divide it in half. Flour the bench scraper again, and make 8-9 cuts widthwise, to get 16-18 small bars.
Once all of the bars are cut, dip the bench scraper or knife in flour again, and VERY gently press it down the center of each bar lengthwise, as far down as you can go without cutting it in half, making a light indentation (this will give the donuts the classic buttermilk bar look).
Fill a large, heavy-bottomed pot or Dutch oven with oil, filling ~2” in the pan. Heat on medium-high until it reaches 350F-370F.
Line a wire cooling rack with a thick later of paper towels.
Once the oil is hot enough, use a bench scraper or spatula to carefully transfer the donuts into the hot oil, 3-4 at a time. Start with frying the donuts with the bottom side down, indentation side up (this will help achieve the look of a buttermilk bar). Fry the donuts for 1-2 minutes on the first side until golden, then gently flip using a metal spatula or a pair of chopsticks, and fry for 1-2 more minutes, until golden.
Using a slotted spoon, carefully transfer the donuts to the rack with paper towels. Repeat with the remaining donuts.
While cooling, make the glaze by whisking together all of the ingredients in a large bowl, until smooth. If the glaze is too thick, whisk in 1 tsp more milk at a time.
Dunk each bar, top side down into the glaze. Set on a cooling rack until the glaze sets.
Serve and enjoy!
