Preheat your oven to 350°F (175°C).
In a mixing bowl, combine the pumpkin puree, sugar, milk, eggs, and vanilla extract. Whisk until smooth and well blended.
Add the ground cinnamon, nutmeg, ginger, and salt to the mixture, and whisk again until incorporated.
Gradually add the all-purpose flour to the mixture, whisking until there are no lumps and the batter is smooth.
Pour the batter into a greased 9x13 inch baking dish, spreading it evenly.
Bake in the preheated oven for about 45 minutes, or until the pudding is set and a toothpick inserted into the center comes out clean.
Once baked, remove from the oven and let cool for a few minutes before serving.
Serve the baked pumpkin pudding warm or at room temperature, optionally topped with whipped cream or a scoop of vanilla ice cream.