Chop baking bars: Coarsely chop 1 whole (4-ounce) white chocolate baking bar. Set aside, and reserve for folding into cookie dough batter. Coarsely chop remaining ½ (4-ounce) white chocolate baking bar. Set aside, and reserve for pressing into cookie dough balls.

Cream sugar and butter, then add eggs and vanilla: Beat sugar and butter with a stand mixer fitted with a paddle attachment on medium speed until light and fluffy, about 2 minutes. Add egg and vanilla; beat just until combined, about 20 seconds, stopping to scrape down sides of bowl, as needed.

Make cookie dough: Whisk together flour, cocoa, baking powder, salt, and baking soda in a medium bowl. Add flour mixture to butter mixture. Beat on low speed until smooth and combined, about 2 minutes. Add red food coloring gel; beat on medium speed until just incorporated, about 30 seconds. Fold reserved chopped whole white baking bar into batter. Cover bowl with plastic wrap; chill until firm, at least 2 hours or up to 8 hours.

Scoop cookie dough, and add remaining chocolate pieces: Preheat oven to 350°F. Line 2 baking sheets with parchment paper. Remove dough from refrigerator. Scoop 12 dough balls by heaping tablespoonfuls; shape into 1 ½-inch balls. Arrange at least 2 inches apart on 1 prepared baking sheet. (Store remaining dough in bowl in refrigerator until ready to bake.) Press about half of the reserved chopped ½ white chocolate baking bar into tops of dough balls.

Bake cookies: Bake until tops are crackled and edges are set, 9 to 10 minutes. Remove from oven; let cool on baking sheet 15 minutes.

Let cookies cool: Transfer cookies to a wire rack, and let cool completely, about 30 minutes. Repeat process with remaining dough and chopped white chocolate baking bar.