Preheat an oven to 350 degrees F (175 degrees C). Grease a 9x13 baking dish; set aside.
Beat eggs until fluffy in a large bowl. Stirring constantly, pour in melted margarine. Stir in sugar, whole kernel corn, and cream-style corn until well combined. Dissolve the cornstarch in the milk; combine with the corn mixture. Stir in vanilla. Pour the mixture into the prepared baking dish.
Bake in the preheated oven until the pudding is puffed and golden, and a knife inserted into the center comes out clean; about 1 1/2 hours.