What's causing this to happen? This is my first Elodie; several blooms are looking like this.

This is normal for Elodie. It is a "double" Asiatic lily that can vary somewhat. Stamens are converted to petals or "petaloids" where they are flattened like petals and sometimes curled like that. In an extreme case they are so petal-like that there will be no pollen and the bloom will be sterile in that respect.

That's a pretty example. If we could stabilise the expression in that form we could have anemone-centred lilies, like we do with Helleborus.