In the bowl of a stand mixer, combine warm water, yeast and about 1 tsp of the sugar. Let this sit for about 5 minutes, or until foamy.
Add the warm milk, cream, the remaining sugar, egg, and salt. Stir this until the ingredients are incorporated. Attach the dough hook to the stand mixer.
Add 3 cups of flour, one cup at a time, beating at low speed to incorporate the flour after each addition. Add the remaining cup of flour, and starting on slow speed, beat the mixture until the flour is moistened. Gradually increase the mixer speed, and beat for 5-8 minutes, until the dough starts to gather in the center of the bowl.
Beat for 5-7 minutes more on high speed, until the dough starts to slap the sides of the mixer with actual slapping sounds. You can sprinkle up to 3-5 tbsp. of flour gradually to help the dough release from the bottom of the bowl. The dough should now be elastic and smooth.
Shape the dough into a ball. Place it in a bowl and cover with a clean kitchen towel. Let this rise for 1 ½ hours, or until doubled in bulk. Meanwhile, make the custard filling.
Gently deflate the dough. Shape it into a log and cut unto 16 equal portions. Flatten each portion into a flat circle using your palms. Spoon about 1-2 tablespoon of custard in the center. Fold the edges of the dough over the filling. Twist the seams to seal, shaping the dough into a smooth ball.
Transfer the remaining custard into a piping bag fitted with a straight piping tip. Arrange the filled dough into a light 9x13 inch baking pan that is lined with parchment paper, spacing them evenly. Cover the dough with a clean towel and let it rise for 40 minutes to 1 hour, or until the buns are now touching and are puffy.
Preheat the oven to 350 F. Pipe the remaining custard on the surface of the risen buns, drawing a spiral design (see photos in the post). Bake the custard buns at 350 F for 25-30 minutes, it until the tops are lightly golden. Brush with melted butter. Enjoy warm.