Mix the ingredients together for the tangzhong and whisk over low heat until it starts to thicken. Let cool for 5 minutes.
Melt the butter in the microwave or in a pan and let cool slightly.
Mix the rest of the ingredients together using your hands or the dough hook attachment with a stand mixer. Add the cooled butter and tangzhong.
Knead the dough for 10 minutes until a smooth dough is formed.
Shape the dough into a ball and place into a lightly floured large bowl. Cover with plastic wrap and let sit at room temperature for 45 minutes to 1 hour.
Once the dough has risen about 60%, degas the dough by pressing out any air pockets. Cut the dough into 6 equal pieces for large buns or 8 for smaller buns.
Put the shaped burger buns onto trays lined with parchment paper. Cover lightly with plastic wrap and let sit for another 45 minutes to 1 hour at room temperature.
Preheat the oven to 350°F/175°C.
Once the buns are ready to go, whisk an egg in a small bowl and brush this carefully onto the buns. Try to get a thin even layer over the top of the buns.
Sprinkle generously with sesame seeds if using.
Bake in the preheated oven for 12-15 minutes or until golden brown on the outside.
You can also use a thermometer to check the doneness of the buns. Once the inside of the buns reaches 200°F, they're perfect.
Let cool on a resting rack for 10 minutes before eating.