In a small bowl, stir together the creamy peanut butter and powdered sugar until smooth and thick. Scoop out 8 small portions, about 1 teaspoon each, and roll them into balls. Place them on a small parchment-lined plate and freeze for at least 30 minutes until firm.
In a large bowl, whisk together the melted butter, brown sugar, and granulated sugar until smooth. Add the egg and vanilla extract and whisk until thick and well combined.
Add the flour, cocoa powder, baking soda, and salt to the bowl. Fold with a spatula until a thick, fudgy chocolate dough forms with no dry streaks. If the dough feels too soft to handle, refrigerate it for 15 minutes.
Preheat your oven to 375F. Line a baking sheet with parchment paper. Divide the dough into 8 equal portions. Take one portion, flatten it in your palm, place a frozen peanut butter ball in the center, then wrap the dough completely around it, sealing all edges. Roll it smooth between your hands.Repeat with the remaining dough and peanut butter balls. Place the stuffed cookies 3 inches apart on the baking sheet.
Bake for 10 to 11 minutes only. The edges should be set but the centers should look very soft and slightly cracked. Do not overbake, as the gooey peanut butter center depends on a short bake time.
Sprinkle flaky sea salt over the warm cookies immediately. Let them cool on the baking sheet for at least 10 minutes. The inside will be molten and gooey when you break them open.