Preheat your oven to 350°F.
In a large mixing bowl, combine the peanut butter, granulated sugar, and brown sugar. Mix until well blended.
Add the eggs and vanilla extract, and beat until smooth.
In a separate bowl, whisk together the baking soda, salt, and flour.
Gradually add the dry ingredients to the peanut butter mixture, stirring until just combined.
Scoop tablespoon-sized balls of dough onto ungreased baking sheets, spacing them about 2 inches apart.
Use a fork to flatten each cookie slightly and create a crisscross pattern on top.
Bake for 10-12 minutes, or until the edges are lightly golden.
Allow the cookies to cool on the baking sheets for a few minutes before transferring them to wire racks to cool completely.