1. Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper or lightly grease it.
2. In a large mixing bowl, cream together the softened butter, creamy peanut butter, granulated sugar, and brown sugar until light and fluffy.
3. Add the eggs, one at a time, mixing well after each addition. Stir in the vanilla extract.
4. In a separate bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add the dry ingredients to the peanut butter mixture, mixing until just combined.
5. Shape the dough into 1-inch balls and place them on the prepared baking sheet, leaving about 2 inches of space between each cookie.
6. Using a fork, press down on each dough ball to create a crisscross pattern. Dip the fork in granulated sugar occasionally to prevent sticking.
7. Bake the cookies in the preheated oven for 10 to 12 minutes, or until lightly golden brown around the edges.
8. Remove the baking sheet from the oven and let the cookies cool on the sheet for 5 minutes. Then, transfer them to a wire rack to cool completely.