In large bowl, stir together flour, baking powder, and salt. In large bowl, beat butter and sugar with electric mixer until light and fluffy, about 2 minutes. Add eggs, one at a time, beating after each addition; add vanilla. Add flour mixture and beat on low until just combined.
Divide dough in half. Form 1 half into 4 in. by 4 in. square; wrap in plastic wrap and set aside. Return other half to mixer; add melted chocolate to dough in mixer and beat just until combined. Form chocolate dough into 4 in. by 4 in. square and wrap in plastic wrap. Refrigerate both doughs at least 30 minutes.
On parchment paper, roll vanilla dough into a 16 in. x 12 in. rectangle about 1/8 in. thick. On another sheet of parchment paper, roll chocolate dough into a 16 in. x 12 in. rectangle about 1/8 in. thick. Place chocolate dough over onto vanilla dough; peel away parchment. Cut dough horizontally in half. Roll each half into a tight log. Roll in colored sugar to coat. Wrap in plastic wrap and refrigerate 3 hours or overnight.
Preheat oven to 350°F. Line cookie sheets with parchment paper. .
Slice logs into 1/4 in. pieces. Space 1 in. apart on cookie sheet. Bake 8-10 minutes, or until vanilla dough is lightly golden.