Each bread machine is different, so place the ingredients into the bread pan as directed by your specific bread machine. Mine says to put the wet on the bottom and dry up top. Select your dough cycle and let the machine do its thing.
When the dough cycle is done, the first rise should have completed. Turn the dough out on to a floured surface and let it rest, covered, for 10 minutes. While that is resting, combine the brown sugar and cinnamon in a bowl and make sure that the butter has been pulled out to soften.
Roll the dough out into a large rectangle, about 16″ by 20″.
Spread the dough with the butter from step two. then sprinkle evenly with the sugar and cinnamon.
Roll the dough into a long tube. Using a very sharp knife, or unflavoured dental floss (go with the floss!) cut the roll into cinnamon buns about 2″ in length. Place the buns about an inch apart in a lightly greased 9″ by 13″ baking pan. I recommend using butter for the greasing.
With a tea towel, cover the buns again and let them rise for 30 minutes. Preheat your grill to 425°F, and prepare for indirect baking.
Turn the grill temperature down to 400°F and bake the cinnamon buns for 15 to 18 minutes, or until the tops are a very light golden brown. Be very careful, they may look under cooked but the longer you bake them, the more the cinnamon-sugar will caramelize. After 18 minutes max, remove the buns from the grill, and allow to cool enough to be eaten. Serve with icing while still warm.
Place the cream cheese and butter into a microwave safe bowl, heat them for about 1 minute. Add the vanilla extract and salt, then the confectioner’s sugar. Using an electric mixer, combine the ingredients until you have a smooth liquidy icing. Be careful, the sugar tends to go everywhere when you turn on the mixer.
Pour generous helpings over your warm cinnamon buns.