Cream together butter and granulated sugar until fluffy, about 3 minutes.
Add eggs one at a time and combine well.
Increase speed of mixer after both eggs have been incorporated. Add in vanilla extract.
In a large bowl, mix together dry ingredients through salt with a whisk.
Using the paddle attachment of mixer, gradually incorporate dry ingredients into butter mixture until all has been combined.
Preheat oven to 350 degrees.
Scoop 2 tablespoons of cookie dough and place onto baking sheet lined with parchment paper.
Gently press cookie dough with the palm of your hand to flatten.
Place into preheated oven and back for 10 minutes. Do not overbake.
Remove from oven and allow to cool on baking sheet while making frosting.
In a large bowl, cream butter. Gradually add confectioners' sugar at 1/2 cup a time.
After each cup has been added, increase speed of mixer to incorporate more air.
Once all sugar has been added, add in vanilla bean paste and mix well.
Gradually add half and half, one tablespoon at a time until frosting reaches a spreadable consistency.
Spread frosting on top of cooled cookies or cookie cake. Decorate with sprinkles (optional) and serve!
