In a stand mixer bowl fitted with the paddle attachment, add the peanut butter, granulated sugar, dark brown sugar, and salt. Beat on medium-high speed until creamy, 45 to 60 seconds. (Don't overbeat or the oil will start separating from the peanut butter).
Beat in the eggs and vanilla until combined, scraping the bowl as needed, about 30 seconds.
Add the flour and baking soda and beat on lowest speed until just combined.
Using a 3-tablespoon scoop, scoop the dough onto a dinner plate (you should have enough for about 13 cookies). Cover with plastic wrap and refrigerate at least 2 hours and up to overnight.
Preheat oven to 375 F (190 C). Line a sheet pan with parchment paper.
Transfer 7 dough mounds to prepared sheet pan. Flatten each mound into a disc about 3 1/2-inches wide (arranging in three rows of one and two rows of two).
Add a heaping tablespoon of marshmallow fluff to the center of each disc.
Seal the fluff within the dough, creating a ball, pinching off excess dough and patching up where needed. (The dough will crack and fluff will leak. This is normal!)
Bake until edges are golden brown and tops are matte, about 8 minutes. (It's okay if they look a little misshapen.) Place the sheet pan on a cooling rack.
Using a deli container, cover each cookie within the container and scoot in a circular motion. This will reshape the cookie into a perfect round. (Make sure to do this as soon as they come out of the oven, while they're still hot).
Let the cookies cool on the sheet pan for 5 minutes. Then transfer cookies directly to the rack and cool completely.
Repeat with the remaining dough and marshmallow fluff.