In a large bowl, cream together butter and sugar until smooth.
Beat in eggs and vanilla. Stir in the flour, baking powder, and salt.
Cover, and chill dough for at least one hour (or overnight).
Preheat oven to 400 degrees F
Separate batter into 3 equal pieces. Tint each piece with a different food gel color (I used orange, black and white).
Pinch away about a tablespoon of each color dough and roll each piece into a log of about 10 inches in length.
Place each colored dough next to each other to form a tri-color rope.
Carefully twist the rope, then coil into a circle (like a snail). Transfer to a parchment lined baking sheet.
Insert a bake safe lollipop stick straight through the middle of the cookie, making sure to pass through all the coils without poking the lollipop stick through the top of the cookie OR you can also place a bake safe lollipop stick behind the cookie and press the cookie into the stick if that is easier for you.
Bake for 6 to 8 minutes. Remove from the oven and allow them to cool for a few minutes, then transfer them to a cooling rack.
Cool completely before serving.