1. Line bottom of 8" by 8" baking pan with waxed paper; set aside. With sharp knife, chop chocolate into small pieces. Place chocolate and shortening in double-boiler top (not over water). Set candy thermometer in place; set aside. Heat water to boiling in double-boiler bottom; remove from heat. Place double-boiler top over hot water; melt chocolate, stirring constantly with rubber spatula until chocolate temperature reaches 130°F.
2. Immediately discard water from double-boiler bottom and refill with cold water. Set top in place and cool chocolate, stirring constantly but gently, until chocolate reaches 83 F. on special 40° to 120°F. thermometer.
3. Meanwhile, in small saucepan over medium heat, heat cream just to boiling; remove saucepan from heat.
4. In small bowl, with mixer at low speed, beat chocolate, cream, and peppermint extract until blended. Increase speed to medium; beat 2 minutes, occasionally scraping bowl with rubber spatula.
5. Pour mixture into prepared pan; set aside until firm, about 2 hours.
6. With metal spatula, loosen chocolate mixture from sides of pan. Invert pan onto cutting board lightly dusted with cocoa; discard waxed paper. Lightly dust sharp knife with cocoa; cut chocolate mixture into 8 strips, then cut each strip crosswise into 8 squares. Store in tightly covered container.