In a large bowl, cream together 1/2 cup butter or margarine, 1/2 cup peanut butter, white sugar, brown sugar, and vanilla. Add egg and beat well.
In another bowl, combine the flour, baking soda, baking powder, and salt. Add these dry ingredients to the creamed mixture. Stir. Add oatmeal and stir.
Drop by teaspoons onto greased baking sheet, and press each mound down with a fork to form 1/4 inch thick cookies. Bake at 350 degrees F (175 degrees C) for 10 minutes, or until cookies are a light brown.
To Make Filling: Cream 3 tablespoons butter or margarine with the confectioners' sugar, 1/2 cup smooth peanut butter, and the cream. Spread filling onto half of the cooled cookies, then top with the other half to form sandwiches.