Add the yeast, warm water, and 1 teaspoon of sugar to a small bowl, whisk, and let it sit for 5 minutes.
Once the 5 minutes are up, combine the milk, egg, remaining sugar, salt, yeast, and melted butter in a large bowl, and whisk by hand. Then, add in the flour, and using the lowest speed on a stand mixer, mix for 6 minutes or until the ingredients are combined, scraping down the sides as needed.
Add a drizzle of olive oil to a large bowl, and toss the dough until it is well coated.
Cover the bowl with plastic wrap or a towel and let the dough sit in a warm, dry place until it has doubled in size. This should take about 1 hour and 15 minutes.
Combine the brown sugar and cinnamon in a small bowl followed by bite-sized pieces of apple.
Roll the dough out into a rectangle that is roughly 24x15 inches. Spread 4 tablespoons of softened butter on top, making sure to reach the edges followed by a sprinkle of the apple and sugar mixture. Drizzle ¼ cup of caramel sauce over the apple filling. Then, with the longest side facing you, roll the dough into a tight sausage shape, and pinch the seam to seal it. Cut the dough in half, and cut each half into 6 equal-sized pieces.
Arrange each caramel apple cinnamon roll in a greased baking dish, leaving space in between. Let them rest for 30 minutes or until they have become fluffy and their edges touch.
Heat the oven to 350 degrees Fahrenheit, and bake for 30-33 minutes or until your cinnamon rolls are fragrant and golden brown on top.
Top the cinnamon rolls with lots of caramel, serve warm, and enjoy!
Notes
The rolls without caramel sauce, aren't too sweet. If you like them extra sticky and sweet, you're going to have to serve them with extra caramel!