Preheat your oven to 350°F (175°C). Lightly grease an 8×8-inch or 9×9-inch square baking dish with butter or non-stick cooking spray to ensure the cobbler serves easily.
In a large mixing bowl, whisk together the flour, baking powder, salt, 3/4 cup of granulated sugar, cinnamon, nutmeg, and cloves until well combined and free of lumps.
Add the pumpkin puree, milk, melted butter, and vanilla extract to the dry ingredients. Stir the mixture with a spatula or wooden spoon until a thick, smooth batter forms. Spread this batter evenly into the bottom of your prepared baking dish.
In a small bowl, mix together the remaining 1/2 cup granulated sugar, the brown sugar, and the chopped pecans. Sprinkle this mixture evenly over the top of the pumpkin batter in the pan.
Carefully and slowly pour the hot water over the entire surface of the sugar and pecan topping. Do NOT stir the mixture. This step is crucial for creating the self-saucing bottom layer.
Place the dish in the oven and bake for 40 to 45 minutes. The cobbler is done when the cake layer has risen to the top and is set, while the sauce underneath is bubbling. Let it stand for 5-10 minutes before serving to allow the sauce to thicken slightly.