Pour salted caramel sauce into the bottom of an 8" or 9" baking dish (like a pie plate or cake pan). Set aside.
Place warm water in a small bowl. Sprinkle the yeast on top of the water. Stir around with a fork or spoon and allow to rest and activate for 10 minutes.
In a large mixing bowl (or the bowl of a stand mixer) with a wooden spoon, blend the milk, sugar, salt, and vanilla extract. Add the egg and yeast mixture and mix again.
Gradually stir in flour. If using a stand mixer, use your dough hook. If mixing by hand, continue to use a wooden spoon. Add 1 and ½ cup of flour, allow dough to come together, then add the softened butter and continue to blend. When butter is mostly incorporated, add the remaining 1 cup of flour and blend until dough has completely come together. It should easily pull away from the sides of your bowl and dough hook or spoon.
Turn out dough on a lightly floured surface and knead until smooth and elastic. Your dough should feel like PlayDoh to the touch and “snap” when you pull it apart. Allow dough to rest for 10 minutes while you prepare the filling.
In a medium size bowl, combine the butter, sugars, cinnamon, and caramel sauce. Stir with a spatula until mostly combined-- some larger chunks of butter are ok. Set aside.
Using a rolling pin, roll the dough out into a rectangle 9" x 12" in size. Dough will be very elastic, so be patient and keep rolling. Using a spatula, spread the filling evenly over the dough, all the way to the edges of the rectangle on all four sides. If you're having trouble spreading the filling, scrape it off and heat it in the microwave for a few seconds to soften the butter further.
ASSEMBLE AND BAKE THE DOUGH
Starting with one of the short sides, roll the dough up into a tight 9" log. Using a sharp serrated knife, cut the log into 6 even slices. Place the slices cut side down in the prepared pan (one in the center and 5 around it), then cover loosely with foil or a kitchen towel and allow to rise for 1 and ½ hours.
When rolls have risen, preheat the oven to 375ºF (191ºC). Place baking dish on a baking sheet, or place a baking sheet on the oven rack under the rolls, as some caramel sauce may bubble over. Bake the rolls for 25-30 minutes or until rolls just start to brown on top. Remove from oven and allow to cool for 5 minutes while you prepare the cream cheese frosting.
CARAMEL CREAM CHEESE FROSTING
In a large bowl with a handheld mixer or the bowl of a stand mixer fitted with a paddle attachment, beat the butter and cream cheese on medium-high speed until smooth.
Turn the mixer speed down to low and add the powdered sugar. Add the salt and caramel sauce and continue mixing until smooth. Set aside.
SERVE THE ROLLS
Get out a serving platter or dinner plate. Being very careful, turn the warm rolls over and out onto the plate. To do this: invert the plate on top of the warm rolls. Using oven mitts, flip everything over (plate is now on the bottom), and allow rolls to settle upside down for a few minutes before removing the baking dish (which is now on top). You may need to shake the baking dish a bit to loosen some parts of the rolls.
Spread cream cheese frosting onto slightly cooled rolls and serve rolls immediately. Drizzle with more caramel sauce, if desired. Leftover rolls stay fresh in an airtight container at room temperature up to 3 days or in the refrigerator up to 5 days. Reheat in the microwave for 8-10 seconds before serving.
*This recipe is for homemade bourbon caramel sauce. You can simply omit the bourbon from the recipe and it will yield plain salted caramel sauce. I strongly encourage homemade caramel sauce here as store bought is typically made with corn syrup which can become chewy and hard in the oven. If you must buy it, look for something without corn syrup.Make ahead: this dough can be made the ahead of time through step 1 of the "assemble and bake dough" instructions. Cover rolls with plastic wrap and allow to rest in the refrigerator overnight. In the morning, remove from the refrigerator and allow to rise in a warm environment, about 1 hour. Continue with step 2 in the "assemble and bake dough" instructions.To freeze: baked rolls freeze well, up to 2-3 months. Thaw overnight in the refrigerator and warm before enjoying.To freeze unbaked rolls: bake the rolls in step 2 in "assemble and bake dough" instructions for 10 minutes at 375°F (191ªC). Allow to cool completely, cover tightly, then freeze. Remove the rolls from the freezer and allow to thaw in the refrigerator overnight. Finish baking for the remaining 20 minutes before icing and serving. To double this recipe: instead of using an 8" baking dish, use a 9" x 13" or larger, roll dough to 12" x 18", and flip out onto a baking sheet or larger platter.To clean everything with hardened caramel on it, soak in warm soapy water to dissolve the sugar.