Begin by melting 4 tablespoons of unsalted butter in a microwave-safe bowl. Heat it in 15-second intervals until fully melted, which should take about 30–45 seconds in total. Set the butter aside to cool slightly while you prepare the dry ingredients.

In a large mixing bowl, whisk together 3 1/2 cups of all-purpose flour, 2 teaspoons of baking powder, 1 teaspoon of kosher salt, 3/4 teaspoon of ground nutmeg, and 1/4 teaspoon of baking soda.

In the bowl of a stand mixer, combine the cooled melted butter, 1/2 cup packed light brown sugar, 1/2 cup granulated sugar, and 1 tablespoon of vanilla extract. Beat the mixture on medium speed until it becomes light and fluffy, which should take about 2–3 minutes.

Add 2 large eggs, one at a time, to the mixing bowl while the mixer is running. Then, add the 1 large egg yolk and 3/4 cup of buttermilk to the mixture and mix until just combined.

Gradually add the dry mixture to the wet ingredients, mixing on low speed until no dry flour remains. The dough should be slightly sticky but manageable.

Cover the bowl with plastic wrap or a clean kitchen towel and refrigerate the dough for at least 30 minutes, or up to overnight.

After chilling, turn the dough out onto a well-floured surface and roll it out until it’s about 1/2 inch thick. Cut into rectangular bars and heat 2 to 3 quarts of vegetable oil in a deep pot or fryer to 360º-365ºF.

Carefully lower the bars into the hot oil, frying them for about 1.5 minutes per side or until they are golden brown.

While the donut bars cool slightly on a wire rack, prepare the glaze by whisking together 2 1/2 cups of powdered sugar, 1/4 cup of water, and 1 tablespoon of vanilla extract.

Once the donut bars are cool enough to touch, dip each one into the glaze, coating them generously. Let any excess glaze drip off before placing them back on the wire rack to set.