Begin by preheating your oven to 350°F.
In a medium-sized mixing bowl, whisk together the all-purpose flour, baking powder, salt, granulated sugar, cinnamon, nutmeg, and cloves until well combined. Set this dry ingredient mixture aside.
Combine the pumpkin puree, milk, melted butter (or vegetable oil), and vanilla in a separate smaller bowl. Mix these wet ingredients until they are thoroughly incorporated.
Pour the wet ingredient mixture into the bowl with the dry ingredients. Stir until a thick batter forms, ensuring there are no lumps.
Transfer the batter to a small 8-inch casserole dish with high sides, spreading it evenly across the bottom.
In another bowl, mix the granulated sugar, brown sugar, and chopped pecans for the caramel sauce. Sprinkle this mixture evenly over the top of the batter in the casserole dish.
Carefully pour the hot water over the entire contents of the casserole dish, being sure not to stir or mix anything.
Place the casserole dish on a baking sheet to catch any potential overflow, and transfer it to the preheated oven.
Bake for approximately 40 minutes, or until the center of the cobbler is set and the top is golden brown.
Remove the cobbler from the oven and allow it to cool for 5-10 minutes before serving.
If desired, serve the Pumpkin Pecan Cobbler warm, garnished with additional pecans and a scoop of vanilla ice cream. Enjoy your delightful fall dessert!