In a stand mixer (using a paddle attachment), cream the sugar and butter until light and fluffy. Add the eggs and vanilla extract; mix.
In a large mixing bowl, whisk together the flour, baking powder and salt. Slowly add the dry ingredients into the stand mixer on low speed; 1/2 cup at a time until the dough has formed.
Take half of the dough out of the stand mixer; set aside. Add red food coloring into the mixer and mix until the dough has turned a deep red hue. Take the red dough out of the mixer; set aside. Put the un-dyed dough back in the stand mixer; add the green food coloring and mix until the dough has turned a deep green hue.
Place one of the dough colors between two sheets of parchment paper and (using a rolling pin) roll into a rectangular shape; about 1/4" thick. Repeat with the other dough color. Put both rolled doughs (including the parchment paper) in the refrigerator and chill for 10 minutes.
Take the top layers of parchment paper off both rolled colored doughs and (using a pastry brush) brush lightly with cold water; the entire surface. Flip one dough on top of the other so both water sides are now touching. Remove the top layer of parchment paper and using a pairing knife, carefully trim the edges to make a straight rectangular shape.
Begin tightly rolling up the dough, using the the bottom layer of parchment paper as leverage to roll and separate at the same time. Continue rolling until you are able to free the bottom piece of parchment paper.
In a shallow baking sheet/pan, pour your holiday sprinkles. Transfer the dough log into the sprinkle pan and roll; gently patting the sprinkles into place until the log is completely covered. Refrigerate for 15 minutes.
Preheat your over to 325°F. Slice the dough log into 1/4" slices and place on parchment lined baking sheets. Bake for 10 minutes. Transfer to cooling racks to cool completely. Store in an airtight container.