Preheat oven to 350 degrees. Line baking sheets with parchment paper, set aside.
Cream butter and brown sugar together until smooth with no lumps. Beat in the egg,vanilla and peanut butter until completely combined. Pour in flour and baking soda and mix until just incorporated without over-mixing. Dough will be very soft and sticky. Chill dough for at least 15 minutes.
Measure granulated sugar into a small bowl and set aside. Roll 1" rounded tablespoons of dough, roll in sugar and place about 1" apart on prepared baking sheet (they don't spread much). Bake cookies for 7-8 minutes. Allow to cool for only 5 minutes on baking sheet and then move them to a wire rack to finish.
These perfect peanut butter cookies will stay soft and fresh for up to 6 days stored in an airtight container.