Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper.
In a large bowl, beat together the peanut butter, softened butter, granulated sugar, and brown sugar with a hand mixer or stand mixer until light and fluffy (about 2-3 minutes).
Add the egg and vanilla extract, beating until well combined.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined.
Scoop rounded tablespoons (or use a 2-tablespoon cookie scoop) of dough onto the prepared baking sheets, leaving space for spreading.
Gently flatten each dough ball into a disk shape.
Bake for 10-12 minutes, or until the edges are lightly golden brown. Let the cookies cool on the baking sheets for a few minutes.
Once slightly cooled, make an indentation in the centre of each cookie. Spoon a generous dollop of marshmallow fluff into each indentation.
Allow the cookies to cool completely on the baking sheets before serving or storing.