In a large mixing bowl, beat the butter on high speed until creamy, about 1 minute.
Lower speed to medium and add the powdered sugar, vanilla extract and salt; continue to beat until combined. Scrape down the sides and the bottom of the bowl as needed. Turn the mixer off and pour in the flour; with mixer on low speed, beat mixture until soft dough is formed.
Pinch off 1 tablespoon of cookie dough and shape into smooth balls. If the dough is too soft to handle, put in the fridge for 10 minutes.
Arrange dough balls about 1-1/2 inches apart on the lined cookie sheets. Using the back of a 1/2 teaspoon measure, press down into the middle of each ball to make a well. If the edges crack, reroll the cookie dough ball.
Bake for 16 to 20 minutes, or until the tops of the cookies are dry and edges are golden brown.
Cool for 5 minutes on the cookie sheet; transfer from cookie sheet to cooling racks. Cool completely, about 20 minutes.
In the meantime, prepare the filling.
FOR THE FILLING
In microwavable bowl, microwave caramels and half-and-half uncovered on High 1 to 2 minutes, stirring once or twice, until caramels are melted.
Spoon caramel into indentation of each completely cooled cookie; let stand about 10 minutes.
Drizzle each cookie with melted chocolate; sprinkle with salt.
Let stand about 10 minutes or until chocolate is set.
Serve.
Notes
HOW TO MAKE AHEAD
Baked, unfilled cookies can be frozen for 1 month. Arrange the cookies in single layers, divided by waxed paper in an airtight container.
You can also keep unfilled cookies on the kitchen counter at room temperature for 5 days.
Cookies can be filled up to 3 days ahead; once filled, arrange on a sheet pan in one layer and cover with plastic wrap. Make sure the plastic wrap isn't touching the caramel. Store at room temperature.