In the bowl of a stand mixer fitted with the paddle attachment, beat butter and confectioners’ sugar at medium speed until smooth and fluffy, 2 to 3 minutes, stopping to scrape sides of bowl. Beat in egg until combined; scrape bottom and sides of bowl. Beat in vanilla.
In a large bowl, whisk together flour, salt, and baking powder. With mixer on low speed, gradually add flour mixture to butter mixture, beating until just combined and no dry streaks remain.
Turn out dough onto a clean surface. Reserve two-thirds of dough (about 640 grams). Tint remaining one-third of dough with food coloring as desired. Wrap colored dough in plastic wrap, and refrigerate until firm, about 30 minutes. Wrap reserved dough in plastic wrap, and let stand at room temperature.
Turn out colored dough onto a lightly floured surface. Roll to ½-inch thickness. Using a 1¼- to 1½-inch holiday cutter (see Note), cut dough, rerolling scraps and cutting to use all dough. Stack cutout dough pieces into 2 (4-inch-tall) stacks, lightly brushing each dough piece with water so they adhere (A). Freeze for at least 30 minutes or up to 1 hour.
Divide plain dough into 10 to 12 portions, and roll each into a 4-inch strip. Place strips around stacks, firmly pressing to adhere plain dough around cutout shape and ensure there are no gaps (B). Start with a small amount of dough and build outward to ensure the cutout shape stays in center of log. Repeat procedure all the way around stacks (C). Gently roll logs, and smooth dough with your hands to seal logs (D). Wrap in plastic wrap, and refrigerate until firm, about 1 hour, or freeze for up to 1 month.
Preheat oven to 350°F (180°C). Line baking sheets with parchment paper.
In separate wide shallow dishes, place nonpareils and sparkling sugar.
Lightly brush egg white onto dough logs. Roll logs in nonpareils or sparkling sugar as desired, gently pressing to adhere. Using a sharp knife, cut logs into ¼-inch-thick slices. Place on prepared pans.
Bake until surface is dry and set, 13 to 15 minutes. Let cool on pans for 10 minutes. Remove from pans, and let cool completely on wire racks. Store in an airtight container for up to 1 week.