Preheat oven to 350°F. Line baking sheets with parchment paper.
In large bowl, cream together butter, brown sugar and granulated sugar until light and fluffy, about 3 minutes.1/2 cup butter,1/2 cup brown sugar,1/2 cup granulated sugar.
Beat in peanut butter until well combined.3/4 cup creamy peanut butter.
Beat in eggs one at a time, then add vanilla extract.2 large eggs,1 teaspoon vanilla extract.
In medium bowl, whisk together flour, baking soda and salt.1 cup all-purpose flour,1/2 teaspoon baking soda,1/2 teaspoon salt.
Add flour mixture to peanut butter mixture and mix until just combined.
Stir in oats until evenly distributed.2 cups old-fashioned oats
Drop rounded tablespoons of dough onto prepared baking sheets, spacing 2 inches apart.
Lightly flatten each cookie with fork in crisscross pattern.
Bake 10 to 12 minutes until edges are set and lightly golden.
Cool on baking sheet 5 minutes, then transfer to wire rack to cool completely.
Notes
Don't add too much flour, or you'll get a dry cookie. I always use the scoop and level method! Also, The fork marks aren't just decorative, they help the thick dough bake evenly.