Pre-heat oven to 350 degrees and place rack in center of oven. Cream together butter, sugars, salt, baking soda and powder. Add vanilla and eggs. Mix well. Add flour and peanut butter chips. Mix just until flour and chips are blended together. Scoop into 2 inch balls and place on a parchment lined cookie sheet about 4 inches apart. Bake for 10-12 minutes.
Peanut Butter Frosting
Cream together room-temperature butter and powdered sugar. Add peanut butter and beat until smooth. Add milk a tablespoon at time, just until frosting is smooth and creamy. Set aside.
Chocolate Frosting
Cream butter and 5 cups powdered sugar. Add cocoa and vanilla. Add milk a tablespoon at a time until frosting is smooth. If needed, add more powdered sugar.
After cookies are cooled, frost with peanut butter frosting. Then frost on top of the peanut butter frosting with the chocolate frosting. When spreading the chocolate frosting on top of the peanut butter frosting, be very gentle and leave a small space between the edge of the peanut butter frosting and the chocolate frosting for a layered frosting look.