Preheat the oven to 350ºF. Place 2 cups of the thawed sweet corn in a blender with the half and half, then blend until mostly smooth.
Add the blended corn to a large bowl with the remaining 2 cups of corn, the eggs, cornmeal, sour cream, sugar, salt, cayenne pepper, and black pepper. Whisk the ingredients together until evenly combined.
Fold 1 cup of the shredded cheddar cheese into the pudding mixture.
Pour the pudding into a greased 2 quart casserole dish, then top with the remaining 1 cup of shredded cheddar.
Bake the pudding for 50 minutes, or until the outer edges are golden and the center jiggles just a little when you shake the dish. Let the corn pudding cool for about 10 minutes before serving.