Preheat the oven to 350 degrees F (175 degrees C). Grease a 2-quart casserole dish lightly (alternatively, a deep 8x8-inch or 9x9-inch pan can be used).

In a medium-sized mixing bowl, sift and combine the all-purpose flour, pastry flour, baking powder, salt, granulated sugar, cinnamon, ginger, nutmeg, and cloves. Once combined, set this mixture aside.

In a separate bowl or large measuring cup, combine the pumpkin puree, milk, cooled melted butter, and vanilla extract. Mix until integrated.

Gradually add the wet ingredient mixture to the dry ingredient mixture. Stir until just combined, ensuring not to overmix. The resulting batter should be thick. Transfer the batter to the greased casserole dish and spread it evenly. Place this dish onto a rimmed baking sheet to prevent any overspill during baking.

For the topping preparation, mix together the granulated sugar, brown sugar, and cinnamon in a small bowl. Incorporate the chopped pecans into this sugar mixture. Evenly distribute this topping over the batter in the casserole dish.

Carefully pour the hot water over the topping. It's essential not to mix or stir once the water has been added.

Place the casserole dish (on the baking sheet) into the preheated oven and bake for approximately 40 minutes, or until the center has set.

After removing from the oven, allow the cobbler to cool for at least 5 minutes before serving. If desired, serve with vanilla ice cream, heavy cream, or whipped cream.