Preheat the oven to 350 degrees. Line a baking sheet pan with parchment paper and set it aside.
Cream the butter and granulated sugar for 1-2 minutes. The butter should be light and fluffy after this first mixing. To this, add the egg yolk and vanilla. Mix this only until the mixture comes together.
Pro Tip: Be sure not to overmix once the eggs are added. This will make the cookies tough. Only mix to combine once the eggs go in.
Combine the flour, baking soda, and salt in a small bowl. Add this to the butter mixture and again, mix only until it comes together.
This batch will make 4 larger cookies, or 6 smaller cookies- this is what I made with my batch. Scoop them onto your baking sheet pan. Press down gently, there is not a lot of spread to these cookies.
Bake for 12 minutes or until the edges are very lightly browned.
Remove the cookies from the oven and let them cool on a cooling rack. They can be enjoyed just like this, or you can follow my example and top them with buttercream.
For the buttercream, combine the butter, powdered sugar, vanilla, and milk. Mix until the icing is smooth. Add more powdered sugar or milk if you want it to be more runny or more stiff. This is a personal choice.
Ice the cookies and add your sprinkles if you are using them.