Step 1 Adjust an oven rack to the middle of the oven. Preheat the oven to 350F [180C]. Line three sheet pans with parchment paper.
Step 2 In a medium bowl, combine the flour, baking soda, salt, and cream of tartar.
Step 3 In the bowl of a food processor fitted with a blade, pulverize the raspberries into a powder. In the bowl of a stand mixer fitted with a paddle, beat the butter on medium speed until creamy, about 1 minute. Add 1 ¾ cup [350 g] of the granulated sugar and beat on medium speed until light and fluffy, 2 to 3 minutes. Add the egg, yolk, and vanilla, and mix again on low until combined, scraping down the sides of the bowl.
Step 4 Add the flour mixture and beat on low speed until just combined. Place the remaining ½ cup [100 g] of sugar in a medium bowl.
Step 5 Dump the dough out onto a work surface and divide it into two equal pieces. Put half of the dough back into the mixer and add chopped white chocolate. Mix on low until totally combined. Remove the dough from the bowl.
Step 6 Put the other half of the dough to the bowl and then add the freeze-dried raspberry powder, and a drop or two of pink food coloring if desired. Mix on low until totally combined.
Step 7 Pinch a portion of each of the doughs, a heaping tablespoon each [25 g]. You can keep the dough this size for a “half and half” cookie, or cut each tablespoon in half to make 4 pieces total. Press the dough pieces gently together, so they adhere to each other, but keep their unique colors (if using 4 pieces, alternate colors in the circle). Press the piece into a cookie scoop or roll it into a ball, then roll the ball into the granulated sugar.
Step 8 Place 6 or 7 cookies on each sheet pan. Bake the cookies one pan at a time, rotating halfway through baking. Bake until the sides are set and the cookies are puffed, 10 to 11 minutes. Transfer the sheet pan to a wire rack and let the cookies cool for 5 to 10 minutes on the pan, then remove them and let them cool completely on the wire rack. Cookies can be stored in an airtight container at room temperature for up 2 days.
