Preheat your oven to 350°F. Line a baking sheet with parchment paper.
In a large bowl, mix together the peanut butter, sugar, brown sugar, vanilla extract, salt, and egg until the batter is smooth and well blended. Cover and allow the cookie dough to rest in the refrigerator for 30 minutes.
After removing the dough from the fridge, scoop about 1 tablespoon of dough and shape it into a ball, then repeat. Arrange the balls on the sheet, leaving about 2 inches of space between each one, and gently flatten each ball with a fork to create a crisscross pattern.
Bake for 8 to 12 minutes, or until the edges are firm. Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a cooling rack.