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.
"It was so cool! They had a mock match, and they had Sadde protecting everyone and she was awesome and the Bludgers were like 'rawr!' but Sadde was like 'nope!' and Arens was like 'gonna score!' but then Greengrass was like 'nope again!' and Sadde's Slytherin friend was really fast and it was awesome you two should've come."
"Our team had a Keeper and me but no Seeker, they had two Beaters and the Seeker, and we scored fourteen times but they scored twice and got the Snitch and the fact that the Snitch is a thing really annoys me."
"Yeah," she sighs. "I mean, if I make the team. I think I will, Hosterforth—that's the other person trying out for Beater—wasn't very good. But in any case on a normal game I'll be allowed to Bludger the other team's Seeker, so."
"Yeah! But today my team didn't have a Seeker and had a Keeper, while theirs didn't have a Keeper but had the Seeker and two Beaters, so my job was protecting the rest of the team from Bludgers so they could actually score. And given that Seekers don't really need to do anything other than fly around, it's much easier for them to evade Bludgers. I think." Shrug.
"That's a weird way to lopside the teams, but I guess it makes sense if you have weird numbers of people trying out..."
"There were two of us trying for Beater, and four trying for Chaser. 'Parently they don't even have reserves."
"If you're only going to have one reserve then in any sane game you'd want it to be a Chaser with three times the odds of needing them, but that's probably smart tactics," sighs Miranda.
"But well it's not like the Chasers actually make that much of a difference in the end for who wins the game, the Seeker is a single point of failure."
"I contemplated coming up with some plot to convince people to get rid of the Snitch altogether but honestly even becoming an animagus is higher priority than that, and if I wanna get social capital there's a significant difference between being a trickster and claiming an international sport is absolutely insane in public."
"In the meantime I'll have fun with evil metal balls and with securing Slytherin the Inter-House Quidditch Cup so that everyone loves me. All part of my diabolical plan. Mwa ha ha."
"Well, not everyone, but the ones who currently think I'm scum are the Slytherins, being generally awesome's good but being specifically awesome at something they care about in particular is better."
"You'll probably make Gryffindors mad at you. Maybe some of the other houses too. But less as a Beater than if you were a Seeker, probably."
"Yeah, and I'm trying to get Slytherins to not hate me and be less horrible, I'm definitely not equipped to fix whatever Gryffindor's problems are."
"I can't claim to understand the sentiment. Flying around is fun, but you can just do that without the evil balls and the mad scoring system."