Preheat your oven to 350°F (175°C). In a medium bowl, combine the graham cracker crumbs, melted butter, and brown sugar. Stir until the mixture resembles wet sand. Press this mixture firmly into the bottom of your greased 8x8-inch baking pan, creating an even crust layer. Bake for 8-10 minutes until set and fragrant.
While the crust bakes, whisk together the pumpkin puree, egg, granulated sugar, and vanilla extract in a large bowl. In a separate bowl, sift together the flour, baking powder, and pumpkin pie spice. Gradually add the dry ingredients to the wet mixture, stirring until just combined. Avoid overmixing to keep the bars tender.
Once the crust is slightly cooled, spread half of the pumpkin batter evenly over the crust. Sprinkle a generous layer of chocolate chips over the batter. Then, carefully spread the remaining pumpkin batter on top. Top everything with marshmallows, pressing them lightly into the batter.
Bake the bars for 25-30 minutes, or until the marshmallows are golden and the pumpkin batter is set around the edges but still soft in the center. Keep an eye on the marshmallows; you may want to switch to the broil setting for the last 1-2 minutes for a perfectly toasted top.
Allow the bars to cool completely in the pan on a cooling rack. This helps them set and makes slicing easier. Once cooled, cut into squares and serve.