In a medium bowl, sift together the flour, baking powder and salt.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter with the sugar until light and fluffy. Add the eggs, one at a time, mixing between each addition, then add the vanilla extract. Add the flour mixture and beat just until combined, scraping down the sides as needed.
Remove half of the dough and pat it into a square. Wrap the dough securely in plastic wrap then refrigerate it.
Add several drops of food coloring to the stand mixer and mix the dough until the color is uniform. Remove the dough, shape it into a square, wrap it securely in plastic wrap and refrigerate it. Allow both pieces of dough to chill in the fridge for 2 hours.
Remove the dough from the fridge. Cut each dough square in half to form four rectangles (two white and two red). Place each piece of dough between two sheets of wax paper. Using a rolling pin, roll each piece of dough into a rectangle that's about 1/8-inch thick. Peel back the top piece of wax paper from each piece of dough then transfer each sheet of red dough on top of each sheet of white dough. (You will have two stacks of dough, each with a red and white layer.)
Starting at the shorter end of each rectangle, roll the dough as tightly as possible into logs. Wrap up the logs securely in plastic wrap then stand each log up inside a glass and place the glasses in the fridge for a minimum of 4 hours. (Standing the dough upright, rather than laying it directly in the fridge, will prevent any flat sides from forming and ensures the cookies will be round.)
When ready to bake, remove the dough logs from the fridge and preheat the oven to 350ºF. Line two baking sheets with parchment paper or Silpats. Using a sharp knife, cut each log into 1/4-inch slices then arrange the cookies on the baking sheets, spacing them about 2 inches apart.
Bake the cookies for 10 to 12 minutes or until they just begin to turn golden brown around the edges. Remove the cookies from the oven and immediately press a candy eye into the center of each cookie. Transfer the cookies to a cooling rack to cool completely.
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