Preheat your oven to 350°F (175°C). Grease a 9x13 inch baking dish and set it aside.
In a large mixing bowl, combine the milk, pumpkin puree, granulated sugar, eggs, and vanilla extract. Mix until the mixture is smooth and well combined.
Gradually add the melted butter while continuing to mix.
In a separate bowl, whisk together the flour, baking powder, salt, and pumpkin pie spice until fully combined.
Slowly add the dry ingredients to the pumpkin mixture, gently folding with a rubber spatula until no lumps remain. The mixture will be thin.
Pour the batter into the greased baking dish.
Place the baking dish on a baking sheet and fill the baking sheet with water until it reaches about halfway up the sides of the baking dish to create a water bath.
Bake in the preheated oven for about 50 minutes, or until the top is golden brown and a toothpick inserted in the center comes out clean.
Once done, remove from the oven and let it cool at room temperature for a bit. Then refrigerate for at least 2 hours to allow the custard to set properly.
Cut into squares and serve chilled or at room temperature.