In a large mixing bowl, whisk together the melted butter, brown sugar, and granulated sugar until smooth and glossy.
Add the egg and vanilla extract, then whisk until fully combined.
In a separate bowl, whisk together the flour, baking soda, and salt.
Fold the dry ingredients into the wet ingredients until just combined. Do not overmix.
Gently fold in the Rice Krispies cereal until evenly distributed throughout the dough.
Cover the dough and refrigerate for at least 20 minutes. Chilling helps prevent the cookies from spreading and makes the dough easier to work with.
Preheat the oven to 350°F and line a baking sheet with parchment paper.
Scoop a portion of dough, flatten it slightly, and place a marshmallow in the center. Wrap the dough completely around the marshmallow, sealing all the edges before rolling it into a smooth ball.
Place the cookie dough balls on the prepared baking sheet, leaving about 2 inches of space between each cookie.
Bake for 11–14 minutes, depending on the size of your cookies, or until the edges are lightly golden and the centers are just set.
Let the cookies cool on the baking sheet for 10 minutes before transferring them to a wire rack. The marshmallow center will be extremely hot straight from the oven.
Enjoy warm for the ultimate gooey marshmallow center!