Bring all ingredients to room temperature.
Preheat oven to 350 degrees F.
Place eggs, corn, sugar, flour and salt in a blender or food processor and pulse until mixture has a hash-like consistency (you should still have some whole corn kernels). Spoon into a 7-by-11 inch glass baking dish.
Melt butter in microwave; set aside to cool.
In a small saucepan, heat milk over medium-high heat until it begins to steam and show small bubbles, but isn’t yet at a full boil (this is also referred to as “scalded” milk). Remove milk from heat and let cool slightly, then gently stir into pudding, mixing well.
Pour melted butter evenly over top of pudding; don’t stir!
Place dish in a larger baking dish with a 1/2 to 1-inch gap between the sides of the two pans. Place on center rack in oven.
Carefully pour hot water into the outer dish, until water reaches around halfway up the sides of the pudding dish.
Bake for around 1 hour. For a more rustic texture, stir pudding from the bottom 2 to 3 times during baking. (Not stirring results in a smoother look and feel.) Pudding is done when set (it can still be a big wiggly in the center).
Remove pudding from oven and water bath; let sit for around 5 minutes before serving. (If your pudding comes out watery or runny, see Tip below from my grandmother to fix.)