Preheat oven to 350F.  In a large bowl, cream together butter, sugar and brown sugar together. Add vanilla, eggs, and 1 cup of the peanut butter; stir to combine. Add oats, flour, baking soda and salt and mix until well combined.

Spray a baking sheet (half sheet pan 17.8 x 12.8 x 1 inch) and spread out dough in an even layer. Bake 15 minutes and remove from oven.

Drop remaining peanut butter (about 1 1/2 cups) by very small spoonfuls over top of warm bars. Set 5-6 minutes and gently spread when peanut butter has begun to melt. It will spread easily when the peanut butter has softened on the warm bars. Don't try to spread it while still thick. Cool bars cool until peanut butter has set up.

Mix frosting ingredients with a hand mixer until smooth and spread on bars. Cut into bars and serve.