Preheat a grill to 350 degrees or medium heat. In a 9-inch cast-iron skillet, melt the butter, then pour into a medium bowl; let cool slightly. Reserve the skillet.
In another medium bowl, whisk together the flour, cocoa powder, ginger, baking powder, pumpkin pie spice, baking soda and salt. In the bowl with the butter, add the brown sugar, eggs, molasses and 1/2 cup water; whisk until smooth. Whisk the flour mixture into the molasses mixture until just combined; scrape the batter into the reserved skillet.
Place the skillet on the grill, cover and bake until springy to the touch in the center, about 25 minutes. Remove the skillet from the grill and increase the heat to 400 degrees or medium-high heat.
Top the gingerbread with the chocolate and marshmallows. Place an inverted 2 1/2-inch-high cake pan, such as a springform pan, on the grill. Place the skillet on top of the pan, cover and bake until the marshmallows are lightly browned, about 5 minutes. Let stand for 5 minutes before cutting.