Cream together butter and 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.
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.
For the Cake:
Spray a 9-inch skillet or cake pan with non-stick cooking spray. Pour cookie dough into skillet or pan and gently spread evenly to all edges of pan.
Bake for 12-15 minutes or just until a toothpick inserted in the center of the cookie cake comes out clean.
Set aside while making frosting.
Cookie Frosting - Vanilla Bean Buttercream
In a large bowl, cream butter. Gradually add confectioner's 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!
Notes
If you do not have Vanilla Bean Paste, you can simply substitute vanilla extract.