Line a 9" square pan with aluminum foil, allowing foil to extend over edges of pan. Butter foil, and set aside.
Butter insides of a heavy 3-quart saucepan. Combine sugar and cocoa in saucepan, stirring well. Stir in milk and corn syrup. Bring to a boil over medium-low heat, stirring gently and constantly with a wooden spoon, until sugar dissolves (6 to 8 minutes). Add 1/4 cup butter, stirring until butter melts. Cover and boil 3 minutes over medium heat.
Uncover and cook, without stirring, until candy thermometer registers 238° (about 14 minutes). Remove from heat. Add remaining 2 tablespoons butter, chopped caramels, nuts, and vanilla. Do not stir. Let mixture cool to 130° (about 25 minutes).
Beat fudge by hand with a wooden spoon until it thickens and begins to lose its gloss (10 minutes). Quickly spread fudge into prepared pan; let cool (about 3 hours). Lift uncut fudge out of pan with foil; discard foil, and place fudge on a cutting board. Cut desired shapes, using 2" cookie cutters, or cut fudge into 1 1/2" squares.