According to Settings->Media, auto-embeds are enabled on the Cooking.SE blog. So, we should be able to embed a YouTube video by just putting the URL by itself on a line, or by using the [youtube=] syntax.
However, neither works.
Nor does using the embed code (iframe version) that YouTube will generate for you (it gets stripped out when you save).
Please enable embeds on Cooking. I hear Photo wants it as well, so if you made that settings checkbox actually work...