Preheat oven to 375 degrees; Line a cookie sheet with parchment paper or spray lightly with nonstick cooking spray.
In a large mixing bowl, cream the butter and brown sugar until light and fluffy with an electric mixer.
Add eggs and vanilla; continue beating until mixed thoroughly.
Add baking soda and pudding mix; continue beating until combined.
Slowly add flour, beating slowly with mixer (mixture will be thick) and set aside while making filling.
In a small bowl combine peanut butter and powdered sugar; mix with wooden spoon until thoroughly mixed.
Lightly flour your hands and make a ball the size of a walnut from the chocolate mixture; pat into a circle in the palm of your hand; Make a small dime-size ball from the peanut butter filling and put in the middle of the chocolate cookie; roll into ball, keeping peanut butter filling in the middle.
Place 3” apart-you may only get 6 larger cookies on the cookie sheet; Bake 8-10 minutes-do not overbake, but make sure your finger indentation in the center remains.
Remove from oven and let set 2 minutes until removing to cooling rack; Let cool 5-10 additional minutes. Makes about 36 large cookies.