Preheat oven to 175°C (350°F) and line a baking tray with parchment paper.
Melt butter in a small pan over medium heat, stirring occasionally until it bubbles and turns amber, about 2 minutes.
Transfer the browned butter to a mixing bowl and cool in the freezer for 5 minutes.
Stir in light brown sugar, granulated sugar, milk, and vanilla extract until fully combined.
Sift in flour, baking soda, and salt, mixing until just a few streaks of flour remain.
Fold in most of the Teddy Grahams and chocolate chips gently until combined.
Top the dough surface with marshmallow fluff, swirling gently.
Cover and place the dough in the freezer for 5 minutes to firm.
Roll the dough into a large ball and place on the prepared baking tray.
Spread extra marshmallow fluff on top and press in remaining chocolate chips and graham pieces.
Bake for 14 to 16 minutes until edges are golden and center appears set.
While hot, use a bowl curved around edges to round the cookie.
Press a large marshmallow on top and toast with a culinary torch if desired.
Let rest for 5 to 10 minutes before serving warm.