In a large mixing bowl, cream the peanut butter, butter and vanilla together until smooth.

Add the sugars and cream for one more minute.  Then, mix in the eggs one at a time. Mix in the flour half at a time.

Wrap the dough in plastic wrap and refrigerate for at least 2 hours.

Once chilled, roll or scoop the dough into 1 1/2-inch balls, and place 2 inches apart on an ungreased or silicon-lined baking sheet.

Use a fork to flatten each ball by making a crisscross pattern.

Bake for 15 minutes or until golden.  Remove cookies from oven, and let cool on the baking sheet for 5 minutes.  Transfer to a cooling rack with a spatula, and allow to cool to at least warm before serving.