Line standard-size muffin pan with baking-cup liners. Place chocolate and cocoa in medium bowl. Pour boiling water over mixture and whisk until smooth. Set in refrigerator to cool completely, about 20 minutes.
Whisk flour, sugar, salt, and baking soda together in medium bowl; set aside. Whisk oil, eggs, vinegar, and vanilla into cooled chocolate-cocoa mixture until smooth. Add flour mixture and whisk until smooth.