In a stand mixer bowl equipped with the paddle attachment, cream the butter and sugar on medium speed until smooth, 3 to 4 minutes. Beat in the egg and vanilla until well incorporated, scraping down the bowl's sides as necessary.

In a medium bowl, whisk the flour, salt, and baking soda together. With the mixer running on low, add the flour mixture in stages and beat until just combined. Take the dough out of the bowl and split it into thirds.

Put one third of the dough back into the mixing bowl, add red gel food coloring, and beat until the color is uniform. Remove the dough, clean the bowl, and repeat with a second third of dough and green gel food coloring. Leave the last third of dough uncolored. Form each portion into a ball, wrap in plastic, and chill for 1 hour.

Take the dough out of the refrigerator and roll each ball between two sheets of parchment paper into a 7-inch square. Chill again for 15 minutes, leaving the dough between the parchment sheets.

Layer the dough sheets on a piece of parchment paper, beginning with red, then green, then plain. Place another piece of parchment paper on top and roll out into a 12x8-inch rectangle. Remove the top parchment sheet. Starting from one long side, tightly roll the dough into a log. Wrap the log in parchment paper and freeze for 1 hour.

Heat the oven to 350°F (175°C). Line two baking sheets with parchment paper and set aside.

With a serrated knife, slice the dough log into 1/3-inch thick pieces. Roll the edge of each slice in red sanding sugar. Arrange slices 1 inch apart on the prepared baking sheets.

Bake for 8 to 10 minutes, or until set. Allow the cookies to cool on the baking sheet for 1 minute, then move to a wire rack to cool completely. Once cooled, pack and store in an airtight container.