In a medium mixing bowl, add the milk, sugar, and yeast and stir to combine. Make sure the milk is warm but not hot, as too hot liquid can kill your yeast. Let the mixture sit for 5 - 10 minutes until the yeast becomes active and frothy.
Add the heavy cream, egg, bread flour, all purpose flour, and salt to the bowl. Using a stand mixer fitted with a dough hook, mix together on low speed until a cohesive dough forms. Then, while the stand mixer is running, add pieces of butter to the dough. Change speed to medium-low and knead for 15 minutes until the dough is smooth and passes the window pane test. You can also do this step by hand.
Cover with plastic wrap and place in a warm area to rise for about 1 hour until doubled in sized.
While the dough is rising, prep the filling. Take 2 tbsp of red bean paste and shape into a ball. Place on a sheet of parchment paper. Repeat until you have 16 balls of red bean paste. I recommend chilling your red bean paste in the fridge beforehand to make it easier to handle.
Make the mochi. Mix together the glutinous rice flour, sugar, and water in a bowl. Microwave for 30 seconds, then give the ingredients a stir. Microwave for another 30 seconds, then stir again. Microwave for a final 30 seconds until the mochi is cooked. It should be translucent and solid. Let cool for a minute or 2 before handling.
Sprinkle the mochi generously with corn starch to avoid sticking. Divide into 16 equal pieces. Place one piece of mochi on top of each ball of red bean paste.
Line 2 baking trays with parchment paper in preparation for the buns.
Once the dough has finished proofing, punch down to release the air. Turn onto a lightly floured surface and divide into 16 equal pieces. To be extra precise, you can use a food scale - each dough ball should weigh about 64g. Shape each piece into a ball. Use a rolling pin to roll into a circle 4 - 5 inches wide, making sure that the center is thicker than the edges. To do this, push the rolling pin with your dominate hand. Use the other hand to rotate the dough in a circle so that you only ever flatten the edges.
Place the filling in the center of the wrapper, mochi side down. Gather the dough and pinch to seal. Gently shape into a perfect round ball and place on the baking tray. Make sure to space at least 1 inch apart.
Preheat the oven to 350°F. Let the buns proof for another 30 - 45 minutes. When you gently press an index finger into the bun, it should only fill halfway.
Whisk together the egg and milk to create an egg wash. Brush the tops of the buns generously with the egg wash and sprinkle the center with black sesame seeds. Bake for 20 minutes until a light golden brown.
Remove from the oven and enjoy!