In a medium-sized bowl, add the flour, baking soda, baking powder, and salt, mix to combine, set aside.
In a large bowl using a stand or hand mixer, cream together the butter and sugar until combined. Add the egg and vanilla, mix to combine. Slowly add the dry ingredients, alternating with the milk until fully incorporated. Start with 3 tablespoons of milk, if dough seems dry add the last tablespoon.
Place in the fridge at least one hour to chill, I suggest waiting overnight if you can. Preheat oven to 375 degrees.
Roll dough into 1 tablespoon sized balls and place on a parchment or silicone lined baking sheet about 2 inches apart. Bake for 8-10 minutes, until the edges are slightly golden brown, do not over bake. Let cool 2 minutes on the tray and move to a wire rack to cool completely.
Place butter in the bowl of a stand mixer with paddle attachment. Mix on low speed until smooth and fluffy, about a minute.
Add in the sifted powdered sugar a spoonful at a time over low speed. Turn up the speed to medium until fully incorporated. Keep doing this until all of the sugar is added, scraping down the sides if necessary.
Add the salt and stir to combine, add in the vanilla and stir to combine. Add in the milk and whip the frosting for 3-4 minutes until light and fluffy.
Divide frosting into equal parts. I used four colors, so I divided it into four separate bowls. I used Wilton Icing colors in sky blue, pink, violet, and lemon yellow. Add a TINY bit at a time, seriously like the end of a toothpick dipped in, and mix it together until you get the color you want.
Frost cookies generously, add sprinkles if desired.