Add 1 cup softened unsalted butter and ⅔ cup granulated sugar to a large bowl and beat on medium-high speed with a hand mixer or a stand mixer fitted with the paddle attachment for 2-3 minutes, until light and fluffy.
Add 1 large egg and 1 tablespoon vanilla extract and mix again until fully combined, scraping down the sides and bottom of the bowl as needed.
Add 2 cups all-purpose flour and ½ teaspoon salt and beat at low speed until fully combined and all the flour has been absorbed.
Use a small cookie scoop to portion the dough into balls and lay them out on one or two parchment-lined baking sheets. Use the back of a 1-teaspoon measuring spoon to press an indent into the center of each ball. Place the baking sheets in the refrigerator to chill for 30 minutes to 1 hour.
About 15 minutes before the dough is finished chilling, preheat the oven to 375 degrees Fahrenheit.
Arrange the chilled dough on parchment-lined baking sheets so there is 2 inches between each cookie, then bake for 8-10 minutes, until the centers of the cookies still look slightly underbaked, but have lost their sheen and turned matte.
Remove the cookies from the oven and immediately use the same 1-teaspoon measuring spoon to reform the indent in the top of the cookie since it will puff up while the cookies bake. Let the cookies cool on the baking sheet for 2 minutes before transferring them to a cooling rack to finish cooling.
Meanwhile, heat 24 soft caramel candies and 2 tablespoons heavy cream in the microwave in 15-20 second increments, stirring between each increment until they are fully melted and smooth.
Use a teaspoon to fill the indentation in each cookie with caramel, about ½ teaspoon or so. Warm the caramel for 5-10 seconds in the microwave as needed to keep it liquid enough to spoon into the cookies.
Melt 4 ounces milk chocolate melting chocolate in the microwave in 30-second increments, until fully melted and smooth, stirring between each increment. Add the melted chocolate to a small ziplock bag, then barely snip the corner of the bag off, and quickly drizzle the chocolate over the tops of the cookies. Sprinkle with coarse salt, if desired, and let them sit until the caramel and chocolate is fully set.
Notes
Storage Instructions
Storage: Airtight at room temp for up to 5 days; use parchment between stacked cookies.
Freezing: Best Method: freeze unbaked (scooped + indented) up to 3 months; bake from frozen, adding 30–60 sec if needed. Or freeze baked, filled, drizzled cookies in layers with parchment up to 3 months; thaw 1–2 hours (caramel may weep).