Preheat your oven to 350°F (175°C). Lightly grease a 9x13-inch baking dish.
In a large bowl, whisk together the flour, 1 cup of granulated sugar, baking powder, all spices, and salt.
In a separate medium bowl, whisk the pumpkin puree, milk, melted butter, and vanilla extract until smooth.
Pour the wet pumpkin mixture into the dry ingredients and stir just until no dry streaks remain. Do not overmix. Spread the batter evenly in the prepared baking dish.
In a small bowl, combine the light brown sugar, the remaining 1/2 cup of granulated sugar, and the chopped pecans. Sprinkle this mixture evenly over the batter.
Carefully and slowly pour the very hot water over the entire surface of the topping. Do not stir the layers together.
Bake for 40 to 45 minutes, or until the top is golden brown and the center is mostly set. The center may still be slightly soft beneath the crust.
Let the cobbler cool in the pan for at least 10-15 minutes before serving. The sauce will thicken as it cools.