You know how sourdough bread gets its complexity from a "mother starter"? This is the mother the madeleine never knew it had.
This winsome cake/cookie is adapted from Dorie Greenspan's Earl Grey Madeleine recipe in BAKING: From my Home to Yours. The stroke of genius is steeping the tea in melted butter for 15 minutes, a trick Dorie learned from tea masters at Mariage Freres. The matcha positively blossomed into a deep green, algae-like paste -- the mother, as it were.
Fat, of course, absorbs and enhances flavor molecules. I can see using similar mother butter infusions for all types of baking -- hibiscus shortbread, mate chocolate chip cookies, and with a butter resolidifing stage, maybe a croissant still light and flaky, but with a perfume of something strong but hauntingly absent.