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.
"But not everything you grew up thinking of as fantasy exists, and not everything you think of as sci-fi will ever exist, either, so it's still not a very good set of categories. Not that they're very good for categorising fiction anyway, soft sci-fi is basically science-themed fantasy."
"Well, technology works, I guess, but 'magic' also includes a lot of stuff I still think doesn't exist."
"Exactly! That's why I don't have anything better, 'magic' is exactly the same as fantasy."
"It does, that's what it means! It's only even as a book genre that it means magic in particular."
"Enchanting spaceships to not need fuel. Terraforming planets using Transfiguration. Shielding charms to hold an atmosphere in place."
"Oh." Pause. "That actually makes sense. I wonder if I could do magic around one of Dad's sensors and see if they pick anything up before they break."
"Well, I wonder that, too, but if you want to do it legally you have to wait until you're seventeen."
"Yeah, but thinking about it like that, it actually does make fundamental magical research more appealing, combining magic and technology would be great."
"I have no idea how long it takes to set up covert experiments, so maybe you should mention to your dad we want to do this in a few years, Willow."