Preheat oven to 350°F In a medium bowl, stir together flour, cocoa powder, baking powder, and salt. Set aside.
Combine the 2 cups chocolate pieces and 2 tablespoons of the butter. Cook and stir over low heat until melted. Set aside to cool slightly.
Beat remaining butter on medium speed 30 seconds. Beat in brown sugar. Beat in eggs, one at a time, scraping bowl after each addition. Beat in melted chocolate mixture and vanilla. Beat in flour mixture on low speed. Stir in 1 cup semisweet chocolate pieces.
Drop by rounded teaspoonfuls 2 inches apart onto ungreased cookie sheet. Bake in preheated oven 8 to 10 minutes or until edges are firm and surface is lightly cracked. Let sit 10 minutes and transfer to wire rack; finish cooling. Dip each cookie one-third to halfway into chocolate ganache. Place on wire rack until ganache is set.
Chocolate Ganache: In saucepan, combine whipping cream, 1 tablespoon butter, and granulated sugar. Bring just to boiling, stirring to dissolve sugar. Remove from heat. Place remaining semisweet chocolate pieces in bowl. Pour hot cream mixture over chocolate; let stand for 5 minutes. Stir until smooth. Cool to room temperature.