3/4 cup butter, softened to room temperature
1/2 cup plus 3 heaping tablespoons creamy peanut butter, divided
1/4 cup granulated sugar
1/3 cup firmly packed light brown sugar
1/2 teaspoon vanilla extract
2 1/4 cups all-purpose flour
1/4 teaspoon salt
1/2 cup bottled dulce de leche
Preheat oven to 300 degrees. Beat butter and 1/2 cup peanut butter at medium speed with an electric mixer until creamy; gradually add both sugars, beating well. Beat in egg and vanilla. Combine flour and salt; gradually add to butter mixture, beating at low speed until blended.
Turn dough out onto a lightly floured surface. Roll to 1/4 inch thickness. Cut with small cookie cutters in desired shapes and place 1 inch apart on ungreased baking sheets.
Bake for 35-40 minutes or until edges begin to turn golden brown. Cool 2 minutes on baking sheets. Remove to wire racks to cool completely.
Meanwhile, stir the dulce de leche and remaining 3 heaping tablespoons peanut butter together until smooth. Spread a thin layer onto the flat side of half the cooled cookies, then place the remaining cookies on top, flat side in to make a sandwich.