Beat butter, brown sugar, and egg together in a large bowl until well blended. Slowly add flour and salt; mix well. Cover and refrigerate for at least 1 hour.

Preheat the oven to 375 degrees F (190 degrees C).

Roll dough into 1-inch balls and place 2 inches apart on cookie sheets. Flatten balls with the bottom of a glass dipped in flour. Press a pecan into the top of each dough ball.

Bake in the preheated oven until sides are golden brown, 10 to 12 minutes.