Preheat your oven to 350 degrees. Line your cookie sheet with parchment paper to help with clean up later.
In a medium-sized bowl, stir together the granulated sugar, the brown sugar, the salt, and the baking soda.
Stir in the peanut butter, the egg, and the vanilla extract one at a time, mixing well after each addition.
Add the chocolate chips and stir well.
Use a cookie dough scoop or a tablespoon to drop balls of dough onto the parchment-lined baking sheet. Keep the dough balls about an inch apart to keep them from spreading so far that they will stick together.
Moisten your fingertips and press the tops of the cookies flat with your fingers. Sprinkle the tops of the cookies with a bit of granulated sugar. Use the tines of a fork to make criss-cross patterns on the tops of the cookies. You may need to dip the fork tines in sugar to keep them from sticking to the cookies.
Put the baking sheet in the preheated oven and bake them for about ten minutes. Bake the cookies until they are lightly browned on the edges. Do your best not to over-bake these cookies, or they will be hard, dry, and crumbly.
When the cookies come out of the oven they will be very crumbly and fragile. Do not touch the cookies while they are hot and fresh from the oven or they will fall apart. Let the cookies cool on the baking sheet for at least ten minutes before you try to scoop them off with a spatula.
If they are still falling apart when you try to take them off the cookie sheet, wait another five minutes. Remove the cookies to a wire rack and allow them to cool. Store in a container with a tightly fitting lid for up to two weeks.