Pineapple Buns with Chinese Barbecue Pork (Bolo Bao)

Instructions

1. • ½ cup water
   • 2 tablespoons all-purpose flour
     ½ cup cold whole milk
   • 1 large egg
   FOR THE DOUGH: Whisk water and 2 tablespoons flour in small microwave-safe bowl until smooth. Microwave, whisking every 20 seconds, until mixture thickens to stiff, smooth, pudding-like consistency and registers at least 150 degrees F/65.5 degrees C, 40 to 60 seconds. Whisk in milk until smooth, then whisk in egg until smooth.  
2. • 2⅔ cups (13⅓ ounces) all-purpose flour
   • ⅓ cup plus 4 teaspoons (3 ounces) sugar
     3½ teaspoons nonfat dry milk powder
   • 2¼ teaspoons instant or rapid-rise yeast
   • 1 teaspoon salt
   In bowl of stand mixer, whisk together 2⅔ cups flour, sugar, milk powder, yeast, and salt. Add cooked flour mixture. Fit stand mixer with dough hook and mix on low speed until all flour is moistened, 1 to 2 minutes. Increase speed to medium-high and knead until dough is smooth and elastic and clears sides of bowl, 10 to 12 minutes.
3. • 4 tablespoons unsalted butter, cut into 2 pieces and softened
   Fit stand mixer with paddle. With mixer running on medium speed, add butter, 1 piece at a time, beating for 30 seconds after each addition. Continue to mix until butter is fully incorporated and dough is no longer shiny, 1 to 2 minutes longer.
4. Transfer dough to very lightly floured counter. Knead dough briefly to form ball and transfer, seam side down, to lightly greased large bowl. Cover with plastic wrap and let rise until doubled in size, 1 to 1½ hours. (Wash and dry mixer bowl and paddle.)
5. • ⅔ cup plus 2 teaspoons (3½ ounces) all-purpose flour
     ¼ teaspoon baking powder
   • ¼ teaspoon salt
     6 tablespoons unsalted butter, softened
     ⅔ cup confectioners’ sugar
   • 2 large eggs, beaten
   • 2 teaspoons vanilla extract
   FOR THE TOPPING: Meanwhile, whisk flour, baking powder, and salt together in small bowl. Using clean, dry mixer bowl and paddle, beat butter and confectioners’ sugar on medium high speed until light, pale, and fluffy, about 3 minutes. With mixer running, gradually add eggs, then vanilla; mix until smooth, scraping down bowl as needed about 2 minutes. Add flour mixture and mix on low speed until combined, about 30 seconds. Scrape down bowl, then fold ingredients by hand to mix fully. Transfer mixture to 1-quart heavy-duty zipper-lock bag and snip off 1 corner, making hole no larger than ¼ inch (alternatively, transfer to pastry bag fitted with ¼-inch piping tip); set aside until ready to use (do not refrigerate). 
6. • 1¼ pounds Chinese Barbecue Pork filling
   To fill buns: Line 2 baking sheets with parchment paper. Transfer dough to counter and divide into 20 equal pieces (about 1½ ounces each). Working with 1 piece at a time, press dough into 4-inch round on lightly floured counter and drape in muffin tin to form cup shape. Fill dough cup with about 1½ tablespoons pork filling. Pull edges of dough to center and pinch tightly to seal. Transfer bun to counter, seam side down, and rotate gently to form round shape. Repeat with remaining dough pieces and remaining pork filling. Space 10 balls evenly on each prepared sheet. Lightly spray tops of buns with vegetable oil spray, cover with plastic, and let rise until doubled in size, about 1 hour. Adjust oven rack to middle position and heat oven to 375 degrees F/190.5 degrees C.
7. When buns are doubled in size, pipe about 2 tablespoons topping in tight spiral on top of each bun (topping should form circle roughly 2 inches in diameter and ¼ inch thick). Bake, 1 sheet at a time, until topping is golden brown, 14 to 16 minutes, rotating sheet halfway through baking. Transfer buns to wire rack and let cool for at least 10 minutes. Serve.