Cream the butter and sugar: In a large bowl, beat the softened butter and granulated sugar with a paddle attachment or electric mixer on medium speed for about 2 to 3 minutes. The mixture should look smooth, creamy, and slightly lighter in color rather than extremely fluffy.

Add the yolk and vanilla: Beat in the egg yolk and vanilla extract until evenly incorporated. Scrape down the sides and bottom of the bowl so no streaks of yolk remain.

Make the cookie dough: Add the flour and salt. Mix on low speed just until the flour disappears and the dough begins forming soft clumps. Stop mixing once the dough holds together when pressed; overmixing can make the cookies tougher.

Divide and color the dough: Divide the dough into three equal portions, about 255 g each. Leave one portion plain. Knead a small amount of red gel food coloring into the second portion and green gel coloring into the third. Add the coloring gradually until each portion is evenly colored.

Roll the three layers: Place each dough portion between sheets of parchment paper and roll it into a rectangle approximately 7 x 10 inches (18 x 25 cm). Keep the three rectangles as similar in size and thickness as possible. If the dough becomes very soft or sticky, refrigerate it for 10 to 15 minutes before continuing.

Build the swirl: Remove the top parchment from the plain dough. Carefully place the red rectangle over it and peel away its parchment, then place the green rectangle on top. Trim noticeably uneven edges if necessary. Starting from one 7-inch (18-cm) side, roll the stacked dough into a tight log, using the parchment underneath to help guide it. Press gently as you roll so there are no large gaps inside the spiral.

Chill the dough: Wrap the log securely and refrigerate for 2 hours, or until firm enough to slice without flattening. Turn the log over once or twice during the first 30 minutes if necessary to help maintain a round shape.

Prepare for baking: Near the end of chilling, preheat the oven to 350°F (175°C). Line 2 large rimmed baking sheets with parchment paper.

Slice the cookies: Unwrap the chilled log and use a sharp knife to cut it crosswise into approximately ¼-inch (6-mm) slices. Rotate the log slightly every few cuts to help keep it round. Arrange the cookies about 1½ inches (4 cm) apart on the prepared baking sheets.

Bake until lightly set: Bake one sheet at a time for 10 to 12 minutes, until the surfaces look dry and set and the outer edges are just beginning to turn pale golden. Avoid waiting for deep browning, which can dull the red and green colors.

Cool the cookies: Leave the cookies on the baking sheet for 5 minutes so they can firm up, then carefully transfer them to a wire rack. Cool completely for about 15 minutes before serving or storing.