On medium to high speed, beat the butter and shortening in a large mixing bowl for 30 seconds.
Add the sugar, baking powder and salt. Beat until combined.
Beat in the egg, milk and vanilla extract until combined.
On low speed beat in the flour, a little bit at a time. You may have to finish mixing in the flour by hand.
On a clean work surface, or on wax paper, knead in enough red food colouring until you get a deep pink colour.
Wrap the dough in plastic wrap and chill for 3 hours.
Preheat the oven to 375°F. Prepare a baking sheet with parchment paper.
In a small bowl, whisk the egg white and water. Prepare another small bowl with the green coarse sugar.
Roll half the dough on a lightly floured surface until it is ¼ inch thick.
Cut out circles using a 3-inch round cookie cutter. Cut each circle into 4 quarters.
Dip the rounded edge of each slice into the egg white mixture and then the green coarse sugar. Place on the baking sheet.
Continue with the rest of the dough. Before baking, press a few chocolate chips into each cookie.
Bake for 5-7 minutes or until the edges are just slightly beginning to brown.
Let cool completely. Cookies freeze very well!
