Preparation

1. 1. Make the cream dough. Insert the chopping blade into the work bowl of the food processor. Add the flours, sugar, milk power, if using, and salt and process on Low for 10 seconds to sift. Add the butter and pulse in 3-second long bursts until large clumps form. Add the white chocolate and vanilla extract and continue to pulse until dough comes together into a single mass. Do not overprocess.
2. 2. Scrape dough out onto a piece of parchment. Pat down into an even layer. Cover with another piece of parchment and roll out into a 12 x 8-inch rectangle. Transfer dough (still between parchment) to a baking sheet and cover loosely with plastic wrap. Refrigerate to chill, at least 15 minutes.
3. 3. Make the strawberry dough. Put the freeze-dried strawberries into the work bowl of the food processor. Process on High until finely ground, about 30 seconds. Add the flours, sugar, milk powder, and salt and process on Low for 10 seconds to sift. Add the butter and pulse in 3-second-long bursts until large clumps form. Add the vanilla extract and continue to pulse until dough comes together into a single mass. Do not overprocess.
4. 4. Scrape dough out onto a piece of parchment. Pat down into an even layer. Cover with another piece of parchment and roll out into a 12 x 7-inch rectangle. Remove the cream dough from the refrigerator and peel off the top piece of parchment.
5. 5. Use the parchment to flip the strawberry dough onto the cream dough, centering the short edge to leave a ½-inch border of cream dough on either long edge. Press a piece of parchment down onto the strawberry dough. Lightly roll over parchment with a rolling pin to press doughs together. Peel off the top piece of parchment.
6. 6. Starting at the closest long edge, use the remaining underside piece of parchment to help roll the dough into a tight, spiraled log. Wrap log in parchment and refrigerate until very firm, at least 3 hours and up to overnight.
7. 7. When ready to bake, set oven racks to upper and lower positions and preheat oven to 375°F.Line two baking sheets with parchment. Sprinkle a clean work surface with sanding sugar or nonpareils. Remove the log from the refrigerator, unwrap and firmly roll in the nonpareils or sugar until evenly coated. Press with your hands to help any loose granules stick.
8. 8. Using a sharp knife, cut a thin slice off each end of the log (this should be just enough to expose the spiral). Cut the log in half, and then cut each in half. Cut each quarter in half to create eighths. Cut each eighth into 4 equal slices to create 32 cookies. Roll the log away from you as you cut to help keep cookies round. Space cookies 1 inch apart on prepared baking sheets.
9. 9. Bake cookies on lower and upper racks until golden around the edges, about 16 to 18 minutes, rotating pans and switching rack positions halfway. Remove and set baking sheets on a wire cooling rack. Leave on baking sheets to cool completely for texture to set properly. (Cookies can be stored in an airtight container at room temperature for up to 5 days.)