1. Place 4 tablespoons unsalted butter in a small microwave-safe bowl. Microwave on HIGH until melted. Set aside to cool slightly.
2. Place 3 1/2 cups cake flour, 2 3/4 teaspoons baking powder, 1/4 teaspoon baking soda, 1 1/2 teaspoons kosher salt and 3/4 teaspoon ground nutmeg in a medium bowl and whisk to combine.
3. Place the melted butter, 1/2 cup packed light brown sugar, 1/2 cup granulated sugar, and 1 tablespoon vanilla extract in the bowl of a stand mixer fitted with the paddle attachment. (Alternatively, use a large bowl and electric handheld mixer.) Beat on medium speed until fluffy, scraping the bowl with a rubber spatula as needed, about 2 minutes.
4. Reduce the speed to low. Add 1 large egg and 3 large egg yolks one at a time, stopping and scraping down the bowl as needed. Add 3/4 cup buttermilk and mix until combined.
5. Add the dry ingredients all at once and mix just until a few streaks of flour remain. Remove the bowl and continue mixing by hand until there are no dry bits of flour. The dough will be quite sticky. Refrigerate at least 1 hour and up to overnight. The rest in the fridge makes the dough easier to work with: it remains sticky, but firms up considerably.
6. Line two rimmed baking sheets with parchment paper. Heavily flour a work surface and your hands with cake flour. Transfer half of the dough to the work surface and sprinkle it with flour. Pat the dough into a 3-by-24-inch rectangle with the long side facing you, adding more flour to the work surface as needed. The dough is extremely soft and sticky, so don’t be afraid to use as much flour as you need.
