Whisk together cake flour, baking powder, salt, nutmeg, and baking soda in a bowl. Set aside.

In a separate large bowl, whisk together both sugars and melted butter.

Add eggs, egg yolk, and vanilla to the sugar mixture; whisk to combine.

Whisk in the buttermilk.

Add dry ingredients to wet mixture; fold until just combined (will be sticky).

Cover and chill in the fridge for at least 30-60 minutes.

Heavily flour a surface and your hands. Lay the dough out, sprinkle with more flour, and gently roll into a large rectangle (18x3.5"; ½" thick), adding more flour as needed.

Use a floured bench scraper to cut the dough lengthwise to divide it in half.

Make 8-9 cuts widthwise to get 16-18 bars.

Gently press the bench scraper down the center of each bar lengthwise without cutting in half, making a light indentation.

Fill a large pot or Dutch oven with oil, approximately 2" high.

Heat oil on medium-high heat until it reaches 350F-370F.

Line a wire rack with a thick layer of paper towels.

Carefully transfer donuts into hot oil, 3-4 at a time, starting with the bottom side down and indentation side up.

Fry the donuts for 1-2 minutes on each side until golden.

Using a slotted spoon, carefully transfer the donuts to the paper towel-lined rack.

Whisk together powdered sugar, browned butter, maple syrup, milk, vanilla paste, and salt for the glaze. Add more milk if too thick.

Dunk each bar in glaze and place on a cooling rack until glaze sets.

Serve and enjoy.