Preheat the oven to 350°F and line two large baking sheets with parchment paper.
In a large bowl, beat together peanut butter, butter, and brown sugar with a hand mixer until smooth and creamy, about 2-3 minutes.
Scrape down the sides of the bowl, add egg and vanilla extract, then mix until combined, about 30 seconds.
Add flour, cornstarch, and kosher salt to the bowl, mixing on low speed until just combined, 30 seconds to 1 minute.
Using a 2-tablespoon cookie scoop, drop dough onto lined baking sheets and flatten each dough ball into a 3-inch disk.
Spoon about 1 tablespoon of marshmallow fluff onto the center of each dough disk.
Fold the dough up around the marshmallow fluff to cover completely and form a ball, placing it back onto the baking sheet.
Bake cookies for 10-12 minutes until edges are brown, watching carefully to avoid burning the marshmallow.
Allow cookies to cool and rest for 10-15 minutes before serving.