To make the dough: In the bowl of a stand mixer fitted with the dough hook, add the yeast, 1/2 teaspoon cane sugar, and warm water. Allow to sit for 5 minutes or until bubbly.
Melt the butter and milk together. You can do this over the stovetop or in the microwave.
Add the flour, 57 grams cane sugar, sea salt, and cinnamon to the yeast mixture. Add the egg and the milk mixture over the top.
Knead on speed 2 to 4 for about 5 minutes or until the dough is smooth.
Transfer the dough to a mixing bowl and cover with plastic wrap. Allow to rise for 1 to 3 hours or until doubled in size.
Preheat the oven to 350°F.
To make the filling: Chop the apple into tiny chunks. I leave skin on, but you can peel if you prefer. Set aside.
In a mixing bowl add the butter, light brown sugar, and cinnamon and mix together.
On a lightly floured surface turn out the dough and roll into a rectangle that’s about 12 x 16-inches.
Using a butter knife or spatula spread the butter mixture all over the rolled out dough. Spread the chopped apples on top of the butter mixture.
Starting at the longer end, roll the dough into a log. Trim off the edges, then cut the log into 8 pieces. Place in a 9-inch pie pan.
Bake for 50 minutes or until the rolls are golden brown and the center looks done. These will take a bit longer than my traditional cinnamon rolls because the apples add more moisture.
To make the glaze: Add the powdered sugar, caramel sauce, and milk to a medium mixing bowl. Whisk together until a smooth glaze forms. Spread over the top of the rolls.
Store in an airtight container in the fridge for up to 3 days.