In a large bowl, whisk flour, baking powder, and salt. In the large bowl of a stand mixer fitted with the paddle attachment (or in another large bowl using an electric mixer), beat butter and granulated sugar on medium-high speed until creamy. Add egg and egg yolk and beat until incorporated. Scrape down sides and beat in vanilla. Add dry ingredients and beat again until just combined.

Transfer one-half of dough to a work surface. To remaining dough in bowl, add cocoa powder and beat until just combined.

Shape each half of dough into rectangles that are 2" tall and wide and about 5" long, making both as close to the same size and shape as possible. Wrap each half in plastic wrap and refrigerate until chilled, at least 1 hour or up to 2 days.

Cut each log into thirds lengthwise. Cut each piece into thirds lengthwise again (you should have 9 long strips from each block). Tim any rounded edges to help make perfect squares.

Place a strip of vanilla dough, then a chocolate strip, then another strip of vanilla right next to each other. Stack a piece of chocolate, then vanilla, then another chocolate on top. Stack a third row of vanilla, chocolate, and another vanilla. Repeat to make a second block of dough, starting with chocolate. Wrap doughs in plastic wrap and refrigerate until chilled, at least 1 hour or up to 2 days.

Preheat oven to 350°. Line 2 baking sheets with parchment. Cut dough into ⅓"-thick squares and arrange on prepared sheets.

Bake cookies until edges just start to turn golden and centers feel set, 10 to 12 minutes. Let cool on wire racks.

Make Ahead: Cookies can be made 5 days ahead. Store in an airtight container at room temperature.