As you may have guessed, I didn't find an egg that was nearly that size. It was smaller than a hen egg, in fact. It wasn't even a full egg - it was half of an eggshell. White, speckled with brownish-black blotches. That's a little bit of a common egg decoration among birds.
The egg from both angles.
There's a hole in the wall and a pair of house sparrows keep flying into it, so perhaps this was a hatched chick's egg fallen out of the hole. On the other hand, it might be the remains of an egg that was eaten by another bird.
I managed to identify it as a house sparrow egg not too long later.