In the large bowl with a mixer, cream together butter and powdered sugar, and mix until the butter is light in color and well blended.
Mix in the egg and vanilla.
Blend in 2 3/4 cups flour, baking powder, and salt. (only add the additional 1/4 cup flour if needed, the dough should be supple and soft not dry)
Mix until the dough forms a ball, on medium speed.
Divide the dough in TWO EQUAL portions.
Mix 1 portion with red food coloring, until desired color is achieved.
Scoop or divide out 1 tablespoon of cookie dough from each color.
Roll each color into a 5 inch "snake" shape.
Place one color "snake" on top of each other and roll them together smoothly until they form 1 "snake"
twist gently to swirl the colors together.
Place on parchment lined baking sheet.
Create the hook shape on one end.
Preheat oven to 400° (you want the oven to be VERY hot when you go to place the cold cookie sheet in the oven)
Once the tray is full, place in the fridge for 20 minutes. (I prepare all the trays, refrigerate all the trays at once, clean up, then bake the trays one at a time)
Remove from fridge, mix the egg white and water, brush each cookie with the egg wash, and add the sprinkles.
Bake for 7-10 minutes, the bottoms will be lightly golden, the tops should not brown.
Remove from oven and allow the cookies to completely cool on the baking sheets.
Baked cookies can remain on the counter overnight, or in a sealed container on the counter for a week, or freeze for 3 months.