Why is this very bad? Because the milk is in direct contact with the heating element, unlike with a saucepan where there's a layer of metal between the element and the milk that will dissipate and evenly spread the heat. The milk right at the element heats to over its boiling point before it can convect away, and thus deposits gunk on the element that traps the heat and burns. Never put anything in an electric kettle except drinkable water.
Oven cleaner did the trick. I used a standard generic brand in a spray can that contains lye/sodium hydroxide or similar, the usual stuff with the slightly lemony nasty odor.
Wear eye protection or be very careful when using oven cleaner! Lye/sodium hydroxide in your eye(s) can cause permanent blindness!
I emptied and dried the kettle.
Gave it about eight seconds' worth of spray of oven cleaner so that the element was coated and the area under it.
Closed the kettle and left it overnight to allow the oven cleaner to work.
Filled with water enough to cover the element, closed to prevent splashing. Gave a couple of shakes to dislodge the loose gunk (looked away too just in case!) and emptied.
Filled with water enough to cover the element, used a long wire brush to get rid of more of the gunk. Emptied.
Filled with water enough to cover the element, shook, emptied. Repeated 3x or until no more gunk was coming out.
Filled with water enough to cover the element, plugged the kettle in, boiled the water to test the kettle and get rid of any remaining trace of oven cleaner. Emptied.
Filled with water enough to cover the element, boiled water, made coffee. Yum.
It's completely fixed, as good as new. Hope this helps someone out.
