Preheat the oven to 350 degrees Fahrenheit and line cookie sheets with nonstick baking liners or lightly spray with nonstick baking spray.
In the bowl of an electric mixer, cream together butter, granulated sugar, eggs and vanilla extract until creamy and fluffy and well blended.
In a separate bowl, whisk together flour, baking cocoa, baking soda and salt.
Add flour mixture to the wet mixture and mix just until incorporated.
Stir in 1 c. chocolate mint baking pieces by hand.
Scoop or form dough into 1 1/2" balls and place at least 2" apart on prepared baking sheets.
Bake for 7 minutes or no more than 8 minutes.
Allow cookies to cool on the cookie sheets for a few minutes before carefully removing them to cooling racks to cool completely.
After they're cool, melt about 3/4 c. chocolate mint baking pieces in the microwave and stir until smooth, then drizzle over the cookies and let set and cool completely. Store in an airtight container.