Begin by preheating your oven to 350°F (175°C). While the oven heats up, prepare a baking sheet by lining it with parchment paper to prevent sticking.
In a large mixing bowl, combine the softened butter, brown sugar, and granulated sugar. Use an electric mixer on medium speed to cream these ingredients together for about 2-3 minutes, or until the mixture becomes light and fluffy.
Next, add the egg and vanilla extract to the bowl. Mix on low speed until the egg and vanilla are fully incorporated into the butter-sugar mixture.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add this dry mixture to the wet ingredients, mixing cautiously until just combined to avoid overmixing.
Gently fold in the chocolate chips and the crushed graham crackers using a spatula, ensuring an even distribution throughout the dough.
To form the cookies, take approximately 1 tablespoon of dough and flatten it slightly in your palm. Create a small well in the center and place 3-4 mini marshmallows into this well. Then, cover the marshmallows with another tablespoon of dough, sealing the edges thoroughly to encase the filling. Repeat this process with the remaining cookie dough.
Arrange the stuffed cookies on the prepared baking sheet, ensuring they are spaced about 2 inches apart to allow for spreading during baking.
Bake the cookies in the preheated oven for 10-12 minutes. The edges should be lightly golden, while the centers may appear slightly undercooked—this is intentional as it contributes to the gooey texture once they cool.
Allow the cookies to rest on the baking sheet for 5 minutes before gently transferring them to a wire rack to cool completely.