Add the softened butter to the bowl of a stand mixer fitted with the paddle attachment.
Beat on medium-high speed for approximately 4–5 minutes, until the butter is very light, fluffy and pale in color.
Scrape down the sides and bottom of the bowl.
Reduce the mixer speed to low and gradually add the sifted powdered sugar, about 1 cup at a time.
Mix until fully incorporated, scraping the bowl as needed.
Pour in 1/2 cup of completely cooled homemade caramel sauce.
Add the vanilla extract and sea salt.
Mix on medium speed until the caramel is evenly incorporated into the buttercream.
Increase the mixer speed to medium-high and beat for another 2–3 minutes until the buttercream is smooth and fluffy.
If the buttercream is too thick, add heavy cream 1 tablespoon at a time until you reach your desired consistency.
For a smooth cake finish, I recommend keeping the buttercream slightly firmer than you would for piping cupcakes.
Turn the mixer to low speed and mix for 1–2 minutes to help remove larger air bubbles.