Using a bowl of a stand mixer fitted with a paddle attachment, combine sugar, butter and vanilla extract. Cream butter on medium speed until light and fluffy.
Add egg and mix until well combined.
Add all purpose flour and salt to bowl. Mix on low until and dough will come together in a crumbly texture.
Add 1-2 tablespoons of milk to the dough and mix on low until fully absorbed.
Use a 2 tablespoon cookie scoop to scoop out 6 pieces of cookie dough and place on a plate, or alternatively use a 3 tablespoon cookie scoop and scoop out 3 pieces of cookie dough.
Take first ball of dough and add 1-2 drops of red food dye, and work thoroughly until well combined. Repeat for all colors.
Scoop 2 tablespoons of dough, and press between palms to flatten and expand dough. It should be about 3" - 4" in diameter.
Remove ½ teaspoon from each colored dough and roll into a cylinder shape. Lay on top of flattened uncolored piece on the far left. You will repeat this process with each color and layer each color piece next to each other.
Gently fold the uncolored portion of the dough over the colored portioned of the dough, and then use hands to roll into ball until seamed together.
Coat thoroughly in sprinkles and place on cookie sheet fitted with parchment paper. Place cookies at least 3" apart.
Preheat oven to 375 F. Bake cookies for 15 minutes, or until you see light browning along edges.
Remove from oven and place on wire rack to cool.