I'm glad you enjoy eating these mushrooms! They are similar to the Shaggy Parasols (Cholorphyllum brunneum) that I have been eating this autumn. They used to even be put in the same genus, but that's changed with more genetic research. In the US, the whole Macrolepiota genus is still being figured out. I think a key for any of these parasols is testing the spore color. No green spores allowed! :O

Do you ever put the stems of the unopened parasols into water, like a flower, to allow them to open up more and get bigger? Or do you use them like that?

I'd really like to read more in your posts. I think you have a lot of experience to share about your mushroom foraging! Enjoy your mushrooms!