Preheat the oven to 175°C. Poke the sweet potato with a fork a few times and bake until soft in the center, about 40 minutes. Let cool, then scoop out the flesh and puree in a food processor until smooth.
Turn the oven down to 95°C (to keep cooked waffles warm). Preheat a waffle iron to medium-high if there are settings (but it's ok if there aren't any). Whisk together the flour, baking powder, baking soda, cinnamon and salt in a medium bowl. Whisk together the buttermilk, 1/2 cup of the sweet potato puree, the oil, brown sugar, egg and egg white. Pour the buttermilk mixture into the flour mixture and gently stir until just incorporated (it's okay if there are lumps).
Lightly brush the top and bottom of the waffle iron with oil, then fill each section about three-quarters of the way full (there should still be some waffle iron showing). Close and cook until the waffles are golden brown and slightly crisp, 6 to 10 minutes. Keep the waffles warm in the oven or covered with foil on a plate while you repeat with the remaining batter.
Switch the oven to broil, and drizzle each waffle with a little syrup and 1/4 cup mini marshmallows. Grill until golden, 15 to 30 seconds.