For dough, in a large mixing bowl, beat the butter with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar, brown sugar, baking powder, and salt. Beat until combined, scraping sides of bowl occasionally. Beat in egg, the 2 tablespoons creme de menthe, the milk, and vanilla. Beat in as much of the 2-3/4 cups flour as you can with the mixer. Stir in any of the remaining 2-3/4 cup flour. Divide dough in half. Cover; chill about 3 hours or until dough is easy to handle.
Meanwhile, for filling, in a medium mixing bowl, combine cream cheese, powdered sugar, the 1/4 cup flour, and the 1 tablespoon creme de menthe. Beat with an electric mixer on low to medium speed until smooth. Stir in a few drops red food coloring until filling is pale pink. Gently fold in crushed candies. Cover and chill up to 2 hours. (Do not chill longer than 2 hours or the candies will bleed into the filling and the filling will become too soft and sticky.)
On a lightly floured surface, roll a portion of the dough into a 12x8-inch rectangle. Spread half of the filling over the dough rectangle to within 1/2 inch of each long edge. Roll both long edges, scroll fashion, to meet in center. Brush seam where dough spirals meet with water; lightly press together. Repeat with remaining dough and filling. Wrap rolls in plastic wrap. Place rolls on a tray or cookie sheet. Freeze for 4 hours to 24 hours or until rolls are firm.
Preheat oven to 350 degrees F. Line cookie sheet with parchment paper; set aside. Using a serrated knife, cut rolls into 1/4-inch slices. Place slices 2 inches apart on prepared cookie sheet. Bake in preheated oven about 10 minutes or until edges are firm and bottoms are lightly browned. Transfer cookies to a wire rack and let cool.