Sift the flour, baking powder and salt (if using) together. Keep aside.
In a bowl, beat the butter and sugar well. Add the egg, vanilla, milk, peppermint extract (if using) and beat until incorporated. Gradually add the dry mixture, beating until combined.
Divide this into 3 portions. Add red colour into one portion and green into another. Mix well till the colour is uniformly distributed. The dough will be slightly wet.
Take a parchment paper or clingfilm. Take one dough portion and place on the sheet. Place another sheet of parchment paper on top of the dough and roll the dough into 1/4" thick rectangular shape. This way you wont have to deal with sticky dough. Keep aside.
Similarly roll out the remaining dough portions into similar sized rectangles using parchment papers.
Place the red colour sheet along with the base parchment paper on the working surface. Carefully lift the plain dough along with the parchment paper and place on top of the red dough sheet, with parchment paper coming on top. Carefully peel off the paper. Similarly place the green sheet on top of the plain dough and peel off the paper. Now we have the red, white and green dough stacked atop each other.
Refrigerate them for 30 minutes to an hour. I would recommend you to touch and feel the dough. If it is slightly firmed up, you can start working on it. If too firm, it may crack while rolling. But you can always stick them back.
Carefully roll the stack into a log shape. If using sprinkles, spread the sprinkles generously on a big tray and roll the log uniformly. The sprinkles will get stuck to it. Cover the log with clingwrap and refrigerate for 1 hour. Slice into 1/4" thickness. Place on a baking tray lined with parchment paper, 1" apart. Bake in a preheated oven at 180C for 10-15 minutes.