Preheat your oven to 350°F (175°C). Line a 9x9-inch baking pan with parchment paper, leaving a slight overhang for easy removal, and set aside.
In a medium saucepan over medium heat, melt the butter. Continue cooking, stirring often, until it turns golden brown and smells nutty, about 5–7 minutes. Immediately pour into a large mixing bowl to cool slightly.
Whisk the brown sugar, granulated sugar, and vanilla into the browned butter until well combined. Add the egg and pumpkin puree, whisking until smooth.
In a separate bowl, whisk together the baking powder, baking soda, salt, and flour. Gently fold the dry mixture into the wet ingredients until just combined.
Fold in the chopped milk chocolate bar and crushed graham crackers,reserving a small handful of each for topping.
Spread the batter evenly into the prepared pan, reserving about 1⁄2 cup of the batter. Arrange the halved marshmallows and pieces of the Hershey’s bar evenly over the top. Drop spoonfuls of the reserved batter over the marshmallows and chocolate, leaving some areas exposed for a gooey top. Sprinkle with the reserved crushed graham crackers and chocolate pieces.
Bake for 35–40 minutes, or until the edges are golden brown and the center is set.
Allow the bars to cool completely in the pan before lifting them out with the parchment overhang. Slice into 9–16 squares and serve.