Cover two cookie sheets with parchment paper. Set aside.
Place all of the ingredients for the buns in your bread machine mixing bowl in order listed. Turn the machine on the dough setting. Turn the machine on and allow it to do its thing (about two hours).
When the bread machine is done, remove the dough and set on lightly floured surface.
Divide the dough into about 18 pieces. Shape into round, slightly flat buns, then flatten slightly so you can stuff them. Stuff the middle of each one with 3 to 5 pieces of caramel bits and 3 to 5 chocolate chips. Then pull up the sides and stretch the dough so the caramel bits and chocolate chips are inside the dough, sort of like stuffing a calzone. Place on parchment lined cookie sheets. Cover and allow to rise for 30 minutes, so they double in size.
Preheat oven to 350°F.
Combine 1 egg and 1 tablespoon of water in a small bowl, whisk until combined. Brush this on the buns, lightly. Make cuts into buns to make little crosses.
Place the cookie sheets in the oven, bake at 350°F for 15 to 18 minutes.
Remove from oven when they appear golden.
For the Glaze:
Combine ingredients in a small bowl, whisk until combined. You can add more confectioners’ sugar if it needs to be thicker, or you can add more milk if it needs to be less thick.
Now drizzle with the glaze while the buns are still warm if you are eating them hot. If you prefer to serve them at room temperature you can allow them to cool completely on wire cooling rack.
Then make thick icing instead of a glaze, all you do is increase the amount of confectioners' sugar to get a thicker consistency. Put in a piping bag and pipe little crosses on each bun.
Serve with a big old caramel and chocolate loving smile!