Preheat oven to 350°F (175°C).
In a large bowl, mix together peanut butter, granulated sugar, and brown sugar until creamy.
Add egg and vanilla extract; beat until combined.
In a separate bowl, whisk together flour, baking soda, and salt.
Gradually add dry ingredients to wet ingredients, mixing until just combined.
Roll dough into 1-inch balls and place on an ungreased baking sheet about 2 inches apart.
Use a fork to gently press down on each ball, creating a crisscross pattern.
Bake for 10-12 minutes or until edges are lightly golden.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Stack cooled cookies on a round white ceramic plate for serving.