Unroll the sheet of crescent dough onto a lightly floured cutting board.
In a small bowl, mix together the softened butter, brown sugar, and cinnamon to form a paste.
Use a spatula to spread the butter/sugar mixture over the crescent dough to the edges.
Roll the dough up tightly into a log, rolling along the long edge so that your finished roll is about 14 inches long.
Slice the roll into 12 even pieces.
Place one piece of cinnamon roll into each cavity of a lightly greased mini muffin tin. As you are placing each roll into the muffin tin, press up the center of each piece gently so that the spiral of the cinnamon roll is facing up in the muffin tin rather than concave down into the muffin tin.
Bake for 10 to 12 minutes, until the cinnamon rolls are lightly browned and cooked through.
Whisk together the glaze ingredients. Dip the top of each cinnamon roll into the glaze and set it on a serving platter.