1.In the bowl of a mixer, add the heavy cream, milk, 1 egg, 1/3 cup sugar, flour, yeast, and salt. Use the dough hook attachment, and turn on the mixer to “stir.” Let it go for 15 minutes, occasionally stopping the mixer to push the dough together. Cover the bowl with a damp towel and place in a warm spot for 1 hour. The dough will grow to one and a half times its original size.
2.Put the dough back in the mixer and stir for another 5 minutes to get rid of air bubbles. Dump the dough onto a lightly floured surface, and cut it into 12 equal pieces.
3.Roll out each piece into a rough oval/rectangle shape, and lay the ham and cheese on top. Roll everything together into a log, and cut three slits into the top of each bun, about 1/2 inch deep. Continue assembling until all the buns are made. Cover with a clean, damp towel and allow to rise for another hour.
4.Preheat the oven to 350 degrees F. In a small bowl beat 1 egg and 1 teaspoon water. Brush the risen buns with egg wash and bake for 20-24 minutes until golden.
5.In a small bowl combine 2 teaspoons sugar and 2 teaspoons of hot water. Mix until sugar has dissolved. Remove buns from the oven and brush the buns with sugar water to give them a really great shine.