Step 1

To make the dough: Whisk together all of the dry ingredients, then add the butter, vanilla, egg, and milk, mixing until a shaggy dough forms. If you're using mashed potatoes add them along with the wet ingredients.

Step 2

, Knead the dough — by hand, using a mixer, or in a bread machine set on the dough cycle — until it's smooth and soft, though still slightly sticky.

Step 3

, Place the dough in a greased bowl, cover the bowl, and let the dough rise until it's almost doubled in bulk, about 1 1/2 to 2 hours. While the dough is rising, make the filling.

Step 4

, To make the filling: In a medium saucepan, toss the grated apple with the lemon juice.

Step 5

, Whisk together the sugar, cornstarch, salt, and cinnamon and add to the pan, stirring to combine.

Step 6

, Cook the apple mixture over low heat, stirring frequently, until the apple starts to release its juice. Increase the heat to medium and bring to a simmer.

Step 7

, Simmer, stirring, until the mixture thickens, 1 to 2 minutes; drawing a spatula across the bottom of the pan should leave a track that doesn't readily fill in. Remove from the heat and set aside to cool to room temperature; if you want to hasten the process, place in the refrigerator.

Step 8

, To assemble the rolls: Gently deflate the risen dough and turn it out onto a lightly floured or greased work surface. Divide the dough in half.

Step 9

, Roll the first half into a 10" x 12" rectangle. Spread half the filling over the rolled-out dough, leaving a 1/2" margin clear of filling along all sides. If adding chopped nuts, sprinkle them evenly over the filling.

Step 10

, Starting with a long side, roll the dough into a log, sealing the edge by pinching it shut. Repeat with the second piece of dough.

Step 11

, Score each log into 12 equal pieces, about 1" for each slice. Cut the dough at the score marks. Dental floss will give you the cleanest cut: pull off a long piece of floss, loop it underneath the log at the score mark, and pull the ends in opposite directions to cut the dough. If you don’t have dental floss, a bench knife or sharp knife will work. Repeat until you've cut all of the rolls.

Step 12

, Place the rolls cut side up in the well-greased or parchment-lined pans of your choice. Place them close together in a 9" square pan for soft-sided rolls, or on a baking sheet about 2" apart for crustier rolls.

Step 13

, Cover the rolls and let them rise until they're puffy, about 1 to 2 hours. Toward the end of the rising time, preheat the oven to 350°F.

Step 14

, To bake the rolls: Uncover the rolls and bake them for 18 to 20 minutes, until they're lightly browned. When the rolls are fully baked a digital thermometer inserted into the center of one of the rolls (be sure to position the thermometer in the bread, not the filling) should register about 190°F.

Step 15

, Remove the rolls from the oven and allow them to cool slightly while you make the glaze.

Step 16

, To make the glaze: Mix together all of the glaze ingredients, starting with the lesser amount of cream. Add additional cream as necessary to make a thick but pourable glaze.

Step 17

, Drizzle the glaze over the rolls and serve.

Step 18

, Storage information: Store leftover rolls, loosely covered, at room temperature for several days.