They try to establish domain on our pond and the neighbor's nearly every year. From what I've seen----no, they do not build a nest; yes, they lay just one egg.
George--because they are in such incredible supply, we have tried them cooked just about every way imaginable. Most ways they vary from "I'd eat it at gunpoint and then only if I was starving" to "Man, this is pretty tough/strong/oily/[put your own gastronomically-negative adjective here]". However......some years ago while I was preparing my smoker to do some venison shoulders my best friend popped in, very early in the day, with several very fresh goose breasts. They (as in scores, if not hundreds) had been destroying the ground around his bass pond with their poo and he had declared war earlier that year. He knew I was going to smoke venison that day, and suggested we try the goose. So I smoked them over charcoal, probably 4-6 hours (maybe 6-8, it's been 10-12 years or more), and over a bath of apple juice, occasionally basting them with the same. When they were done we shared them with several friends and all agreed it was quite palatable. Never replaced prime rib or bacon on my menu, but it got a very passing grade. Have only done a few since, primarily because it's a pain to dress them out and most of those that die around here do so suddenly and sometimes out of season. Best not to cook those...I'm sure you understand.
