Preheat your oven to 375°F and grease a half-sheet pan with edges, set aside.
In a large bowl, cream together the butter and sugar until smooth and creamy.
Add in the vanilla and eggs. Mixing between each egg addition.
In a medium bowl, combine the dry ingredients: flour, salt, and baking soda.
Add this to the wet ingredients in several additions, mixing between each addition until just combined.
Spread into an even layer on the baking sheet and bake for 12-17 minutes, until the center is set and a toothpick comes out clean. It will also look a light golden brown. Allow the pan to completely cool on top of a baking rack before frosting.
In a medium bowl, use a hand mixer on medium speed to beat the butter until smooth.
Add the vanilla, salt, and powdered sugar. Mix thoroughly until well combined.
Add in 4 tablespoons of milk and mix well. Check consistency – mix in the remaining milk if you want the frosting to be thinner. If you are coloring the frosting, add food coloring to the frosting until you reach your desired coloring.
Layer frosting on top of your sugar cookie bars and add sprinkles if desired.
Cut into bars and serve. The frosting will harden so if you want to stack them on a tray you will want to make sure to give the cookies time for the frosting to set.