Cream butter & sugar until fluffy. Add eggs, one at a time, mixing after each egg. Add vanilla & mix well.
In separate bowl combine flour, salt & soda & stir with whisk to combine. Add to wet mixture and mix just until combined. Spread on a greased baking sheet ( 13 X 18 size). Bake at 375 degrees for 10 to 18 minutes until light golden brown or until a toothpick comes out clean in the middle.
Cool completely before frosting.
Combine butter & shortening until smooth and creamy. Add vanilla and salt. Add powdered sugar in 1-2 cup increments until combined. Then add milk & mix until smooth and spreading consistency. Add food coloring if desired and mix well. Spread over cooled cookie. Decorate with sprinkles if desired.