Beat butter at medium speed of an electric mixer until creamy; gradually add sugars, beating well. Add eggs and vanilla; beat well.
Combine flour, soda, and cocoa; gradually add to butter mixture, beating well. Stir in 1/2 cup pecans. Cover and chill dough at least 2 hours. Combine remaining 1/2 cup pecans and 1 tablespoon sugar.
Divide dough into 4 equal portions. Work with 1 portion at a time, storing remainder in refrigerator. Divide each portion into 12 pieces. Quickly press each piece of dough around a caramel; roll into a ball. Dip one side of ball in pecan mixture. Place balls, pecan side up, 2" apart on ungreased cookie sheets.
Bake at 375° for 8 minutes. (Cookies will look soft.) Let cool 1 minute on cookie sheets; remove to wire racks and let cool completely.