Preheat the oven to 350 F.

Make the dough: Fit a stand mixer with the dough hook and a large mixing bowl. Add the warm milk, yeast, egg, sugar, salt, and melted butter to the bowl. Whisk thoroughly by hand.
Tip in the flour. Turn the stand mixer on at its lowest speed and mix for 6 minutes. You may need to scrape the bowl down once or twice.
After 6 minutes, test the dough by touching it with a clean and dry finger. It should feel slightly tacky but shouldn't stick. If the dough sticks to your finger, add extra flour, a tablespoon at a time, until the dough no longer sticks to your finger. 
When the dough is ready, add a small drizzle of olive oil to a bowl and turn the dough into a bowl. Flip the dough a few times, so it's coated in oil. Cover the bowl with clingfilm and leave it to rise in a warm place. This will take approx 1 hour but might take longer depending on how warm your kitchen is. You are looking for the dough to double in size.
Make the filling: Add the brown sugar and cinnamon to a small and mix. Chop the apples into small bite-sized pieces.
Assemble the rolls: When the dough has risen to twice its size, remove it from the bowl and turn it onto a lightly floured surface. Roll the dough into a roughly 40cm x 20cm rectangle.
Spread the 4 tbsp of very soft butter onto the surface of the dough, then sprinkle over the cinnamon sugar and chopped apples. Drizzle over 1/4 cup of caramel sauce.
Roll the dough with the longest side facing you into a tight sausage shape. Pinch the seam of the dough together with your fingers.
Cut the dough in half and cut each half into six equal pieces. [about 5cm each]
Grease a rectangular baking dish with 1 tbsp butter. Arrange the rolls in the dish, leaving a bit of space in between. Put the dish somewhere warm for 30 mins. During this time, the rolls will puff up and join together.
Bake the rolls in the center of the oven for 35-40 mins or until the rolls are lightly brown. Check on them after 20 minutes; if they are browning too quickly, cover them with foil.
Once baked, remove from the oven and drizzle over 3/4 cup caramel sauce.
Serve while still warm.