Preheat oven to 325ºF. Line an 8x8 inch square baking dish with parchment paper* making sure to leave extra overhanging over the sides so you can lift the caramelies out once they've baked. Spray with nonstick cooking spray. Set aside.

In the bowl of an electric stand mixer fitted with the paddle attachment, cream the butter and sugar together. Add the flour and continue mixing. Add the caramel syrup, egg, cream cheese, salt and vanilla. Mix until fully incorporated, scraping down the sides of the bowl if necessary.

Pour batter into prepared baking dish and bake for 40-43 minutes. Allow to cool completely.

In the bowl of a stand mixer fitted with the paddle attachment, combine the butter, caramel syrup, and salt, blending on low speed just until combined. Add the powdered sugar, 1/2 a cup at a time, mixing between each addition. Scrape down the sides of the bowl, and add the vanilla. Increase mixer to high speed for about 1 minute and blend until buttercream is fluffy and lightened in color.

Using a knife or an offset spatula, spread the frosting evenly over the caramelies. Lightly sprinkle the coarse salt over the top.

Holding the ends of the parchment paper, gently lift the caramelies out of the baking dish and onto a cutting board. Cut into squares and serve.