Cut the kabocha into bite-sized pieces with the skin still attached. Cut off 1 cm corners for decorative purposes and place into a separate heat-resistant container.
Cover with plastic wrap and steam in the microwave until you can cleanly insert a skewer.
Once steamed, remove the skin for the filling and put inside of a bowl. Cool the kabocha for garnishing.
Add white chocolate to the filling-pumpkin, and mix while the heat from the pumpkin melts the chocolate.
Add the ingredients marked with ★ to taste. (The taste of kabocha differs by season and type, so adjust accordingly with granulated sugar.)
Cut a puff pastry into 4 sheets. Use two of the pieces to create a 7 cm round sheet. You can use a cup to help.
Use a fork to punch shallow holes in the remaining two puff pastry. Trace egg whites around the border of the sheets, then place the sheets with the holes removed (created in Step 6) on top of the whole sheets.
Use a fork to punch shallow holes in the bottom layer of the round puff pastry. Add the filling and trace the edges with egg whites. Add the top cover sheet, and use a knife to cut slits in the sides to prevent the filling from spilling out.
Repeat Steps 6-8 with the other puff pastry. Apply egg yoke to the top, careful not to let any on the sides of the sheets (it'll prevent the sheets from inflating).
Bake in the oven at 390°F/200℃ for about 25 minutes.
Use a spoon to fill the squares with filling. Top with the decorative kabocha bits and you're done!