Slughorn explains, when everyone is assembled, that alchemy with an egg is actually where phoenixes are speculated to originate; but no one has the recipe any more and there haven't been new phoenixes for centuries. They will not be making living things today. But the eggshell is a good base from which to appear lots of possible objects; alchemy doesn't like to conjure things into existence in plain sight but is quite willing that new things appear inside eggshells, cocoons, geodes, and similar. Their eggs have been pre-drained of their interiors for this purpose, although some recipes use full eggs.
As last week, they are invited to come up with recipes on paper for review by the professor before trying anything. Known possible results available with this set of ingredients include wooden, decorated eggs nested inside the shell; a shellful of small sharp teeth (the commonest source of hens' teeth, as they have encountered once or twice in potions); successively smaller eggshells the smallest of which holds a blob of mercury; and a perfectly hardboiled egg which can be arbitrarily flavored by exact details of the process. But they are welcome to aim at another result as long as their procedure looks safe.
The paint is dry! Except under the egg, so he turns it around and paints the rest. "And even if it is I still think I'd be able to do it."
"Do you think you wouldn't? If it turned out there weren't clever tricks like 'asking the Professor about it' available?"
"Hmm. No I'm not that thing. That's not what I meant with it. I meant the other thing."
"Well, what's even the point of being... emotionally... patient like that? That sounds terribly boring."
"It seems like it may be more comfortable than our way of doing things in times of boredom."
Eventually their paint is dry and they can move on to their final steps!
Miranda gets a wooden egg. It doesn't have an obvious way to open it, so it's not easy to tell if it might have more inside.
And Sadde drops water from the prism to the egg and tries cracking it to see what he got. "By the way, there's an implication there from what Slughorn said to our little project."
Upon cracking the egg, quite a lot of blue paint starts leaking from it, and Sadde tries to find a place he can deposit an eggful of paint without making a big(ger) mess. Upon doing so he finishes cracking it and a much tinier blue glass egg falls from it. The glass is itself tinted and not painted. "Huh. This is actually pretty neat." He looks up at Miranda again. "Anyway, apparently the metaphor thing is kinda personal so it's very possible that in addition to finding something meaningful you have to be the kind of person that would produce something?"
"Right. But there's no obvious way to find out, and there's different ways to make stuff, so it might be that anybody can make anything if they find the right set of steps."
"Yeah, no, I'm taking that as encouragement, it's another piece of the 'how come no one else ever managed to do it' puzzle that makes it easier to understand while simultaneously not making our attempt doomed from the start."
Professor Slughorn comes by, opens up her egg, finds that it does contain further wooden eggs but they aren't as pretty, and puts them all back together seamlessly for her.
And she shows Professor Slughorn his non-prismatic-but-still-pretty glass egg, beaming.
"Maybe white paint would have got it prismy?" asks Miranda.
"If Mr. Woods would care to retry with white paint another time he may come in whenever I'm in the lab and not overseeing a class to do so."