Let the prepared rolls stand at room temperature for 45 minutes to 1 hour. Meanwhile, position a rack in the center of the oven and preheat to 350 degrees.
Bake the rolls until golden and a toothpick inserted in the center comes out clean, about 30 minutes. Remove from the oven and let cool on a rack for 5 to 10 minutes; invert onto a plate, then invert again onto a cutting board or platter.
Using a fork, stir together the confectioners' sugar, half-and-half, cinnamon and salt. Drizzle the glaze over the rolls and serve warm or at room temperature with the apple mash.