Preheat oven to 350°F. Line 2 baking sheets with parchment paper.
In your stand mixer, use the paddle attachment to cream together the butter and sugar until light and fluffy. If you don’t have a stand mixer, you can use a hand mixer to cream them together in a large bowl.
Scrape down the sides of the bowl and mix in the vanilla. Then add in the egg and the egg yolk, one at a time, mixing until fluffy once again.
In a small bowl, whisk together flour, baking soda and salt. Add this to the wet ingredients, one big spoonful at a time, mixing until just combined. Add in the sprinkles 🎉 and mix on low JUST until they are mixed in.
Using a small cookie scoop (my small one holds about one tablespoon), scoop the dough onto a parchment lined sheet pan, about 2 inches apart. I usually do three rows of four. Or four rows of three. (My larger scoop holds two tablespoons, and I place 6-8 cookies on the sheet pan at a time.)
Bake at 350° for 11-13 minutes (closer to 11 minutes for small cookies, 13 for large ones), or until the edges are just BARELY starting to turn a light golden color and the tops are starting to crack. Allow the cookies to cool on the sheet pan until set, around 5 minutes or so, then transfer to a cooling rack. They will be puffy, but they will relax. Repeat until all the cookies are done. You can taste one, but the rest have to wait for the icing. Nope. Just one.
While the cookies are cooling, and you are definitely not scarfing them all down, let’s make the icing. Takes a few seconds max.
In a small bowl, whisk the powdered sugar, vanilla, salt, and milk until smooth and shiny. If the icing seems too thick to drizzle, add a bit more milk. If it seems too thin, add a bit more powdered sugar.
There are three approaches to drizzling the icing: with a spoon, with the tines of a fork, or from a plastic baggie with a teensy corner snipped out. The first two are more rustic (which is great) and the third is more uniform. Go crazy. Be artistic. Then eat cookies. Happy Birthday (someone)!