Preheat the oven to 350°F (175°C).

In a mixing bowl, cream together the softened butter, peanut butter, granulated sugar, and brown sugar until smooth.

Beat in the eggs and vanilla extract until well combined.

In another bowl, whisk together the flour, baking soda, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Roll the dough into small balls and place them on a baking sheet lined with parchment paper.

Flatten each ball slightly with a fork to create a crisscross pattern.

Bake in the preheated oven for 10-12 minutes or until the edges are golden.

Remove from the oven and let cool on the baking sheet for a few minutes before transferring to a wire rack.

In a mixing bowl, combine the peanut butter, powdered sugar, and vanilla extract until smooth.

Once the cookies are completely cooled, spread a generous amount of the peanut butter filling on the flat side of one cookie.

Top with another cookie, flat side down, to create a sandwich.

Repeat with remaining cookies and filling.