Mix milk and yeast in a bowl.
Add sugar, salt, and eggs, and mix well.
Add cake flour and bread flour, and knead the dough.
Add room-temperature butter and knead until smooth.
Cover the dough with plastic wrap and let rise (first proof).
Divide the risen dough and round into balls.
Shape and place them in the pan.
After the second proof, brush with egg wash.
Bake in a preheated oven at 180°C for 25 minutes.