Use a stand mixer or electric hand mixer to whip together butter, sugar, vanilla and salt.
Add the flour and continue to beat until combined.
Bring the dough together to form a ball. Wrap in plastic wrap and refrigerate for 30 minutes.
Prepare two baking sheets by lining with parchment paper.
Preheat oven to 300°.
Remove the chilled dough from the fridge. Roll into balls about 1 generous teaspoon, and place them about an inch apart, on parchment lined baking sheets. Use a ½ teaspoon measuring spoon, or your thumb, to form a deep well in each ball. Smooth the edges with your finger.
Place the prepared sheets in the center of the oven and bake 20 - 25 minutes, until edges turning golden brown.
Remove from oven and allow to cool about 10 minutes, then transfer to a rack and let the cookies cool completely.
When the cookies have cooled, fill each one with salted caramel sauce. It helps to use a squeeze bottle for this. Don't be tempted to overfill, because the filling will run over the sides.
Allow the filling to set, and sprinkle lightly with fleur de sel, sea salt, or kosher salt.