In a large bowl, whisk together flour, baking soda, and salt.
Using a mixer, cream butter until smooth, about 2-3 minutes.
Add sugars and continue to beat until combined, about 4 minutes.
Add eggs and beat for 2 minutes.
Slowly beat flour mixture into the butter, sugar, and eggs. Add vanilla and peanut butter, and continue stirring until all ingredients are well incorporated.
Chill dough in the fridge one to two hours.
Preheat oven to 375F. Shape dough into 1 inch balls, then roll in granulated white sugar until covered.
Press balls with a fork to flatten cookies.
Bake for 10-12 minutes, or until cookies have browned slightly.
Allow cookies to cool on baking sheet for 10 minutes, then transfer to cooling rack to finish cooling.