Preheat the oven to 350 degrees. Line baking pans with Silpats (French nonstick baking mats); set aside.
In a medium bowl, whisk together flour, cocoa powder, baking powder, and salt; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, cream butter and sugars on medium speed for 1 minute. Beat in egg and vanilla. With the mixer on low speed, add the flour mixture and beat to combine.
Use a 1 1/4-inch ice-cream scoop to form a ball of dough. Place a pecan in the dough, pressing lightly to secure. Place the dough pecan side down onto the prepared baking sheet. Repeat with the remaining dough and pecans.
Using the back of a teaspoon or your thumb, create an indentation in the top of each cookie and fill with 1/4 teaspoon of chopped caramel. Bake until firm, about 15 minutes. Transfer cookies to a rack to cool completely.