I made your broiled polenta bites; followed the directions exactly; when I broiled them, they became too soft to pick up and eat as an canapé. What could be the problem?
Hmm. Did your polenta firm up nicely once you chilled it? Wondering if it was maybe too wet?
Another trick that should keep that from happening is to let the polenta steam in the pot for at least a half an hour after you believe it's "done," with the lid on but the heat off. (I always cook my polenta in a bowl insert that sits on top of a medium saucepan, so the hot water in that pan keeps the bowl/polenta somewhat warm. If doing this in just a single saucepan, I'd probably sit the saucepan in a larger pan filled 1/3 to 1/2 with very hot water. The "double boiler" step though, in my experience, really does produce an exceptional polenta, making it well worth whatever trouble might be perceived.) The extra 30-40 minutes continues the absorption of the liquid by the cornmeal, while giving the polenta a somewhat lighter, almost creamy texture -- one that's neither too dry, nor too wet. The key is keeping the polenta warm during this process. Best polenta ever, no matter what recipe or how you're serving it.
Seriously, this is one of those details that will have your dinner party guests begging to know who you did it. ;o)