Preheat oven to 350˚F. Line cookie sheets with parchment. If oil has separated from the peanut butter, stir until all oil is mixed in and peanut butter has a smooth consistency.
In a large bowl, whisk together sugar, baking soda, and sea salt. Add peanut butter and beaten egg and stir with a large spoon until combined. Stir in chopped peanuts. The dough will be crumbly.
Using a medium cookie scoop, drop 11/2-inch balls on prepared sheets, spacing them 2 inches apart. With the bottom of a glass or back of a spoon, flatten the balls to 1/2-inch thickness.
Bake for 12 to 15 minutes, until golden brown. Lightly sprinkle with fine grain sea salt, if desired. Cool completely on cookie sheets.
Store cookies in an airtight container for up to 1 week.
Baker's Notes: Cashew butter is sometimes less moist than peanut butter. If you substitute cashew butter, you may want to add 1/4 teaspoon vegetable oil prior to mixing.