Whisk the dry base: Stir the cake flour, baking powder, salt, nutmeg, and baking soda together in a large bowl until the mixture is uniform.

Combine wet ingredients: In a separate container, blend the melted butter with both sugars, then whisk in the eggs, egg yolk, vanilla, and buttermilk until smooth.

Form the dough: Gently fold the flour mixture into the wet ingredients with a spatula until just combined, being careful not to overwork the sticky dough.

Chill: Cover the bowl and refrigerate for at least thirty to sixty minutes to make the dough manageable.

Shape the bars: On a heavily floured surface, roll the dough into a large rectangle about half an inch thick, then cut into eighteen bars and press a light indentation down the center of each.

Prepare the oil: Fill a heavy pot with two inches of frying oil and heat until a thermometer reads between three hundred fifty and three hundred seventy degrees.

Fry until golden: Carefully cook the bars in small batches for about two minutes per side until they reach a deep golden brown, then drain on a wire rack.

Brown the butter: Melt the glaze butter in a saucepan over medium heat, cooking until it foams and smells nutty with toasted amber bits at the bottom.

Whisk the glaze: Combine the browned butter with powdered sugar, maple syrup, milk, vanilla bean paste, and salt until it reaches a smooth, dippable consistency.

Finish and set: Dip the top of each warm donut bar into the glaze and return them to the rack to let the coating firm up before serving.