Preheat the oven to 350 degrees Fahrenheit. Line a baking sheet with parchment paper.
Whisk the egg, then whisk in the peanut butter and brown sugar until a smooth dough forms. Chill for 15 minutes.
Make 1 ½ tablespoon-sized balls and place them onto the baking sheet, evenly spaced about 2-inches apart. Roll the balls between your hands to make them as spherical as possible: (if the dough is very sticky, lightly oil your hands to make it easier to roll).
Use a lightly oiled fork to flatten the balls and make a criss-cross pattern (it’s helpful to dip the fork into a small bowl of water before each one to prevent sticking).
Top the cookies with a small sprinkle of flaky salt if desired.
Bake 8 to 10 minutes until lightly browned on the bottom but still soft. Cool completely before serving.