Cut butter into small cubes and set aside. If your kitchen is very warm, I recommend putting it into the freezer while you prep your next steps.
In a large mixing bowl, whisk flour with salt and sugar.
Add in the cubed butter and work the butter into the flour with a pastry cutter or by hand, until the flour resembles coarse sand with some squished lumps of butter remaining. This step can also be done in a food processor.
Add in the cold water and very gently mix by hand until the flour is fully hydrated. Different flours absorb liquid differently, so you may need to add more liquid. If your dough still has some dry flour spots, add 1 tablespoon of cold water at a time until your dough comes together in a ball (but is not wet and sticking to your hands).
Shape dough into a round disc and wrap in plastic wrap. Let chill in the refrigerator 15-20 minutes while you prep your fillings.
Line two baking sheets with parchment paper and preheat your oven to 425 degrees F.
To prepare your filling, scoop 16 portions of roughly 2 tbsp each, or the size of a golf ball. A medium cookie scoop works great for this. Roll into balls and set aside.
Take your pastry dough out of the fridge and cut into 16 equal pieces. Roll each into a ball and gently flatten into a 3-4 inch circle, trying to get the edges thinner than the center. If your dough is sticking to your hands, you can dust with additional flour.
Place one ball of filling in the center of the dough. Wrap your dough around the filling, pinching the edges to seal. Repeat for the remaining 15 portions. Note: Wrapping the filling may take some practice, but you want to handle the dough as little as possible to avoid melting the butter. If you feel that you've made the dough too warm, stick the wrapped manju back in the fridge to chill for another 5-10 minutes before baking. Place manju on your baking sheet.
Whisk egg in a small bowl and brush the egg wash onto the tops of the manju. Optional: If you are using a variety of fillings on one tray, you may want to use different colored sesame seeds or other types of sprinkles to mark which manju has which filling.
Bake at 425 degrees F for 25-30 minutes, or until pastry has turned golden brown. Let cool and enjoy! Leftovers can be kept in an airtight container in the fridge.