Line two baking sheets with parchment paper; set aside.
In the bowl of a stand mixer fitted with a paddle attachment, beat the butter, peanut butter, and sugars until smooth.
Add the egg and beat to combine.
Add the flour, baking soda, and salt; beat until a smooth dough forms.
Fold in the peanuts, reserving 2 tablespoons for topping the cookies, if desired.
Use a 1-ounce portion scoop to portion cookies onto a parchment-lined plate. If you have time, refrigerate for at least 30 minutes, or until firm.
Transfer the scooped cookies to the parchment-lined baking sheets, spacing them a few inches apart. Top with the remaining peanuts and flaky sea salt, if desired.
Bake for 12–14 minutes, until set on the edges but still gooey in the center.
Let stand on the baking sheets 5 minutes, then transfer to wire racks. Drizzle with the melted peanut butter, if desired.