Cream the butter, sugar and brown sugar together in a mixing bowl, using an electric mixer at medium speed, until light and fluffy. Add the eggs one at a time, beating well after each addition. Beat in the peanut butter and vanilla. Sift the flour, baking soda and salt together and stir into the creamed mixture. Form the mixture into 1-inch balls. Place about 2-inches apart on greased baking sheets. Press with floured fork, making a criss-cross pattern on each. Bake in a preheated 375 degree F. oven for 8 minutes or until golden brown. Remove from the baking sheets and cool on wire racks. When completely cooled, spread one cookie with the peanut butter filling and top with another cookie making a sandwich. Makes 3 1/2 dozen cookies. Peanut Butter Filling: Mix all of the ingredients in a medium bowl and beat with an electric mixer at medium speed until smooth and creamy.