Prepare for baking. Preheat the oven to 350°F. Line two baking sheets with parchment paper.
Cream the butter. In a large mixing bowl, beat the butter on high speed until creamy, about 1 minute.
Add the remaining ingredients. Lower the 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 the mixer on low speed, beat the mixture until a soft dough forms.
Shape the dough. Pinch off 1 tablespoon of cookie dough and shape into smooth balls. If the dough is too soft to handle, put it in the fridge for 10 minutes.
Make a well in the center of the cookies. Arrange the dough balls about 1 ½ inches apart on the lined cookie sheets. Using the back of a ½-teaspoon measure, press down into the center of each ball to make a well. If the edges crack, reroll the cookie dough ball.
Bake. Bake for 16 to 20 minutes, or until the tops of the cookies are dry and edges are golden brown.
Cool. Cool for 5 minutes on the cookie sheet; transfer from the cookie sheet to cooling racks. Cool completely, about 20 minutes. In the meantime, prepare the filling.
For the Filling
Melt the caramels. In a microwavable bowl, microwave caramels and half-and-half uncovered on High 1 to 2 minutes, stirring vigorously every 30 to 45 seconds, until the caramels are melted.
Fill the cookies. Spoon the caramel into the indentation of each completely cooled cookie; let stand about 10 minutes.
Drizzle with chocolate. Drizzle each cookie with melted chocolate and sprinkle with sea salt. Let the cookies stand about 10 minutes or until the chocolate is set.
Notes
Stirring the caramels:
Make sure to stir after each interval so the caramel melts evenly and doesn’t get too hot, which can make it turn grainy or firm up. You can also use store-bought caramel sauce.
Make Ahead and Storage:
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.