Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.

In a large bowl, cream together the softened butter, peanut butter, brown sugar, and granulated sugar until smooth. Add the eggs and vanilla, mixing until well combined.

In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Scoop tablespoon-sized amounts of the cookie dough and flatten them slightly. Place a teaspoon of peanut butter in the center of half of the cookies, then top with another flattened cookie to create a sandwich.

Place the filled cookies on the prepared baking sheet and bake for 10-12 minutes or until the edges are lightly golden. Let them cool on the sheet for 5 minutes before transferring to a wire rack.

Melt the chocolate chips in a microwave-safe bowl, stirring every 30 seconds until smooth.

Drizzle the melted chocolate over the cooled cookies and sprinkle with chopped peanuts if desired. Allow the chocolate to set before serving.