Vada's Vanilla Buns

Ingredients

• 1.5 cups unsweetened flaked coconut
• 2.5 cups bread flour, plus extra to dust the work surface
• ½ cup water, plus 1 tablespoon
• 3 vanilla beans
• ½ cup milk (not skim)
• 2 2
• 1 packet (2.25 teaspoons) instant or Rapid Rise yeast
• ¼ cup granulated sugar
• Kosher salt
• 3 tablespoons unsalted butter, cut into 4 pieces and softened

Instructions

1. In a medium skillet over medium heat, toast the coconut, stirring constantly, until many of the flakes are dark golden brown (some flakes will remain white, so the quantity will appear to be spotty brown), about 4 minutes. Immediately scrape the coconut into the bowl of a food processor, and set aside to cool to room temperature, at least 10 minutes. Pulse until it's about the texture of whole flax seeds (a little smaller than sunflower seeds), about five 2-second pulses, and set aside.
2. Meanwhile, carefully wipe out the still-hot skillet. In the skillet, off heat, whisk ¼ cup of the flour and ½ cup of the water until it forms a smooth, thick paste (with help from the residual heat in the skillet) about the texture of mashed potatoes, about 1 minute. Immediately scrape the paste into the bowl of a stand mixer, and set aside to cool until tepid, about 8 minutes.
3. Meanwhile, with a paring knife, halve the vanilla beans lengthwise and scrape the seeds from all six halves. Collect the seeds in a small dish, cover, and set aside.
4. Add the milk to the flour paste and whisk until smooth. Add one egg and whisk to incorporate it. Add the remaining 2¼ cups flour and the yeast. Fit the bowl and the dough hook to the stand mixer and mix on low speed for 1 minute. Adjust the speed to medium-low and continue mixing until the flour is incorporated and the resulting mass is cohesive, about 30 seconds longer. Turn off the mixer and rest the dough for 15 minutes. Add the sugar and 1½ teaspoons salt and knead on medium-low speed for 5 minutes, until the dough appears smoother. With the mixer running, add one piece of the butter and continue mixing until it is incorporated fully into the dough, about 30 seconds, before adding the next. Repeat to add and incorporate the remaining three pieces of butter, adding the vanilla seeds along with the last piece. Continue to mix on medium-low speed 5 minutes longer, adding the coconut midway through that time and stopping when needed to scrape down the dough hook and sides of the bowl (the dough will be quite soft and sticky).
5. Flour a work surface very lightly, scrape the dough from the bowl to the surface, and knead it briefly to form a ball. Lightly oil a medium bowl, add the dough, and turn it to coat very lightly with the oil. Cover the bowl with a clean kitchen towel or plastic wrap and set aside until the dough has become puffy and its volume has increased by three-fourths or doubled, about 1 hour.
6. Oil a 9-inch round cake pan, line the bottom with parchment paper, and oil the parchment paper. Transfer the dough to the work surface, gently deflate it, and press and stretch it into a 10 by 12-inch rectangle with a short side facing you. Cut the dough lengthwise into 4 equal strips and cut each strip crosswise into 3 equal pieces. Working with 1 piece of dough at a time, stretch and press the dough gently to form an 8 by 2-inch strip. Starting on a short side, roll the strip to form a snug cylinder. Arrange the shaped buns seam-side down in the prepared pan, placing 10 buns around the edge of the pan, pointing inward, and the remaining 2 buns in the center. Cover the pan with a clean kitchen towel or plastic wrap and set aside until the buns appear puffy and their volume has increased by about three-fourths or doubled, about 1 hour.
7. When ready to bake, with a rack in the lowest position, preheat the oven to 375°F. In a small bowl, beat the remaining egg with 1 tablespoon water. Gently brush the tops of the buns with the egg wash (take care not to deflate the dough) and bake until deep golden brown, 20 to 24 minutes, rotating the pan halfway through. Set the pan on a cooling rack and cool for about 15 minutes. Gently loosen the edges of the buns with your fingers and gently pry them out of the pan. Cool the buns until just warm or room temperature, remove the parchment from the bottom of the buns if necessary, and serve. Leftover buns can be wrapped tightly and stored at room temperature for up to 3 days.