Preheat Oven: Preheat your oven to 350°F (175°C). Grease a 2-quart baking dish.

Prepare the Mixture: In a large mixing bowl, combine the corn kernels, eggs, milk, melted butter, sugar, vanilla extract, salt, and black pepper. Mix well.

Add Dry Ingredients: In a separate bowl, whisk together the flour and baking powder. Gradually add the dry ingredients to the wet mixture, stirring until just combined.

Pour into Baking Dish: Pour the corn pudding mixture into the prepared baking dish, spreading it evenly.

Bake: Bake in the preheated oven for 45-50 minutes, or until the top is golden brown and the center is set. A toothpick inserted into the center should come out clean.

Cool and Serve: Allow the corn pudding to cool slightly before serving. It can be served warm or at room temperature.