Preheat oven to 350 degrees Lightly grease baking sheet or place parchment paper on top.
Cream together peanut butter, softened butter, granulated sugar and brown sugar with a hand or stand mixer. Add egg and vanilla extract until fully incorporated.
In a separate mixing bowl, add flour, baking soda, and salt and mix well. Slowly add mixture to the creamed ingredients until well combined.
Roll the cookie dough into approximately 1-inch balls and place on cookie sheet, leaving about 2 inches between cookie. Using a fork, press horizontally, then vertically, making a crisscrossed pattern. Be careful not to flatten the dough ball too much. Sprinkle tops with separated sugar.
Bake for about 10-12 minutes, until cookies just start to brown. Let cool before serving.