Preparation Arrange two approximately 12- by 12-inch square pieces of wax paper on a work surface and spread half the flaked coconut in the middle of each. In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and sugar and beat on medium speed, scraping the bowl occasionally, until light and fluffy, about 2 minutes. Add the milk and vanilla or rum extract and beat until fully incorporated. With the mixer on low, add the flour in 3 batches, followed by the red and green cherries and the pecans, and stir until just combined, about 2 minutes. Divide the dough in half and form each half into a 10-inch-long log, about 1 1/2 inches in diameter. Transfer each log to a sheet of wax paper and roll to coat them in the coconut. Once the logs are completely covered in coconut, roll the wax paper around each log, cover in plastic wrap, and chill for at least 1 hour and up to 24 hours. Position a rack in the upper third of the oven and a second rack in the lower third then preheat to 375°F. Slice each log crosswise into 1/4-inch-thick cookies and arrange on baking sheets, leaving about 1 inch between cookies. Bake, switching the baking sheets between the upper and lower racks about halfway through baking, until light golden brown, about 12 minutes. Cool the cookies on the baking sheet for 10 minutes before transferring to a wire rack to cool completely. Continue baking cookies on cooled baking sheets. DO AHEAD: The cookies can be baked ahead and stored, in an airtight container at room temperature, up to 3 days.
Preparation Arrange two approximately 12- by 12-inch square pieces of wax paper on a work surface and spread half the flaked coconut in the middle of each. In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and sugar and beat on medium speed, scraping the bowl occasionally, until light and fluffy, about 2 minutes. Add the milk and vanilla or rum extract and beat until fully incorporated. With the mixer on low, add the flour in 3 batches, followed by the red and green cherries and the pecans, and stir until just combined, about 2 minutes. Divide the dough in half and form each half into a 10-inch-long log, about 1 1/2 inches in diameter. Transfer each log to a sheet of wax paper and roll to coat them in the coconut. Once the logs are completely covered in coconut, roll the wax paper around each log, cover in plastic wrap, and chill for at least 1 hour and up to 24 hours. Position a rack in the upper third of the oven and a second rack in the lower third then preheat to 375°F. Slice each log crosswise into 1/4-inch-thick cookies and arrange on baking sheets, leaving about 1 inch between cookies. Bake, switching the baking sheets between the upper and lower racks about halfway through baking, until light golden brown, about 12 minutes. Cool the cookies on the baking sheet for 10 minutes before transferring to a wire rack to cool completely. Continue baking cookies on cooled baking sheets. DO AHEAD: The cookies can be baked ahead and stored, in an airtight container at room temperature, up to 3 days.