Start by making the matcha-custard filling. Heat whole milk over medium-low heat in a medium saucepan. Add vanilla and continue to heat until steaming and bubbles form around sides, about 5 minutes.
Whisk together egg yolks and sugar in a medium mixing bowl until pale yellow. Add flour and continue to whisk until fully blended into yolks. Turn heat off and whisk in 2 sachets of matcha tea crystals.
Whisking constantly, pour about 1/3 cup of milk mixture over egg mixture. Continue to gradually whisk in milk mixture until combined. Pour mixture back into saucepan and heat over low heat. Whisk constantly as mixture heats. At first, there may be some foam at the top, but as the mixture heats and thickens it will become smooth and deepen in color. After 5-6 minutes, the mixture should be thick like custard. Turn heat off and pour into a small bowl. Cool at room temperature for 20 minutes then place in a bowl in the refrigerator while preparing dough.
To make dough for pineapple buns: Combine 1/3 cup of water with 2 tablespoons flour in a heat-safe bowl. Microwave mixture for 40 seconds. Continue to microwave in 5-second increments until the mixture is thick and paste-like. Set aside on countertop to thicken and cool.
Heat whole milk in a heat-safe bowl for 40-45 seconds. The milk should be between 110-120ºF. Stir in sugar. Add 2 teaspoons of active dry yeast and stir to incorporate. Allow mixture to sit on the countertop for 5-7 minutes until foamy.
In the bowl of a stand mixer, combine flour, salt, tangzhong, sweetened condensed milk, egg, melted butter, and yeast mixture. Using the dough hook attachment, mix dough for 10 minutes on low speed.
Use a spatula to gather the dough and knead on a clean countertop for 30 seconds. Form the dough into a ball and place in a medium greased mixing bowl. Cover with a towel or plastic wrap and place in a warm spot for 1 hour, until the dough has doubled in size.
In the meantime, cream the softened butter in the bowl of a stand mixer or using a hand mixer until smooth. Gradually add superfine sugar while mixing. Add egg, milk, vanilla, and mix on low speed until just combined.
Combine flour and baking powder in a small bowl. Gradually mix flour into wet ingredients. Once mixture resembles dough, turn the mixer off and form dough into a ball. Place in a small bowl and cover. Refrigerate.
Line 2 medium baking sheets with parchment paper. Punch the dough a few times softly to release air. Divide the pineapple bun dough into 2 equal portions. Place 1 portion of the dough in a bowl and cover. Refrigerate while preparing the first batch of buns.
Divide the other dough into 6 equal portions. Knead 1 piece a few times to remove air bubbles. Place into your hand and flatten into a disc about 4-5 inches in diameter. Spoon 1 teaspoon of matcha custard in the center. Seal by pinching the edges of the dough and then pressing the opposite sides together. Form into a ball shape and place on baking sheet. Repeat with the remaining 5 pieces of dough. Cover buns with plastic wrap and allow them to proof for 30 minutes longer.
While buns are proofing, whisk together egg wash in a small bowl and refrigerate.
Once the dough has almost finished proofing, preheat the oven to 375ºF. Form the cookie crust dough into 12 small balls using 1 tablespoon to scoop. Flatten the dough into a disk using hands. Place a disk of dough on the tops of each bun. Use a sharp knife to run over the crust, creating a pineapple grid. Brush the tops with egg wash.
Bake for 18-20 minutes, until the crust on top is light golden brown. Repeat with remaining dough, crust and egg wash. Cool buns on baking sheet for 10 minutes before transferring to a wire cooling rack for 10 minutes longer. Serve slightly warm. Store buns in an airtight container in a dry spot.