Preheat the oven to 350°F and line baking sheets with parchment paper so the cookies do not stick while baking.
In a large bowl, cream together the softened butter and brown sugar until the mixture becomes smooth and slightly fluffy.
Add the egg, vanilla extract, and peanut butter, then mix until everything is fully combined and creamy.
Add the flour and baking soda, mixing gently until just incorporated without overworking the dough.
Scoop portions of dough and roll them into balls, keeping the size consistent for even baking.
Roll the dough balls in granulated sugar if desired, which adds a light crunch on the outside.
Place the dough balls on the prepared baking sheets, leaving space between each one for spreading.
Use a fork to gently press each ball into a criss-cross pattern while keeping the cookies thick.
Bake until the cookies are lightly set and just beginning to turn golden around the edges.
Let the cookies cool on the baking sheet briefly before transferring them to a rack to cool completely.