In a large bowl, beat the sugar and butter with an electric mixer on medium speed until well blended. Beat in the egg and vanilla until light. Mix the flour, baking powder, and salt. Beat the dry ingredients into the butter until the dough is smooth, scraping down the sides of the bowl frequently with a rubber spatula. Divide the dough in half. Remove one half and shape it into a square roll 2 inches on a side; be sure to make the sides flat. Place the remaining dough in a small bowl. With a fork, stir in the chocolate until well blended. Shape the chocolate dough into a square roll, 2 inches to a side. Wrap and refrigerate at least 3 hours or up to 3 days (or freeze up to 6 months).

When ready to bake cookies, preheat the oven to 350 degrees. Lightly grease several cookie sheets. Slice both pieces of dough lengthwise to make four long slices. Reassemble the rolls alternating chocolate and light doughs. Slice the rolls crosswise to make 3-inch thick cookies. Place the cookies 2 inches apart on the prepared cookie sheets. Bake until firm and very lightly browned on the edges, 12 to 15 minutes. Remove the cookies to a wire rack and let cool completely. Store in an airtight container.