Adjust oven rack to middle position and preheat oven to 350°F (175°C). Generously butter a 7-inch round or a 8- by 8-inch baking dish.
In the bowl of a food processor, pulse corn kernels until thick, creamy, and some kernels are still visible, about 20 seconds. Set aside. (See notes.)
In a medium bowl, whisk cornstarch, granulated sugar, salt, and pepper to combine. Add eggs, followed by the corn, milk, and melted butter, whisking until well combined. Pour into prepared baking dish.
Bake, uncovered, until edges are golden brown and the center no longer jiggles, 50 to 60 minutes. Remove corn pudding from oven and allow to rest 10 minutes, or until cool enough to eat. Serve immediately.
