Preheat oven to 375°F (190°C). Line baking sheets with parchment paper.

In a large bowl, cream together the softened butter and peanut butter until smooth and creamy using a hand mixer or stand mixer.

Gradually add the granulated sugar and brown sugar, beating until well combined.

Beat in the eggs one at a time, then stir in the vanilla extract.

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. Do not overmix.

Drop by rounded tablespoons onto the prepared baking sheets, leaving about 2 inches between each cookie.

Use a fork to flatten each cookie slightly, making a criss-cross pattern.

Bake for 8-10 minutes, or until the edges are lightly golden brown. Let the cookies cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.