Preheat oven to 350°F (175°C) and lightly grease a 9x13-inch baking dish.
In a large bowl, combine pumpkin puree, sugar, milk, melted butter, eggs, and vanilla. Mix until smooth and fully combined.
In another bowl, whisk together flour, baking powder, pumpkin pie spice, and salt.
Gradually add the dry ingredients to the wet mixture, stirring gently until just combined.
Fold in the chopped pecans evenly throughout the batter.
Spread the batter into the greased dish and bake for 30–35 minutes, or until the top is golden and a toothpick inserted in the center comes out clean.
Let the cobbler cool slightly before serving warm.