In large bowl, cream butter and sugar until light and fluffy. Add eggs, one at a time, beating well after each addition. Stir in vanilla. Combine flour, baking cocoa, baking powder, baking soda and salt. Add to creamed mixture alternating with yogurt. Beating well with each addition. Fold in zucchini and carrots.
Fill paper-lined muffin cups 2/3 full. Bake for 18-22 minutes or until toothpick comes out clean. Cool for 10 minute before removing from pans to wire racks to cool completely.
Frosting: Beat butter on medium until smooth. Gradually add powdered sugar; beat until light and fluffy. Melt chocolate chips and add to butter mixture. Beat at medium until smooth.