Champagne chicken

Where have I been all my life? I never knew, until PieLady mentioned it in another thread, that champagne chicken was even a thing. Since then, I've started testing, and so far, I think, it's real, and it's spectacular!

Well, to be honest, it's basically chicken in a tarragon cream sauce, which is a combination I already loved, based primarily on Nigel Slater's recipe in his book, The Kitchen Diaries. Between his recipe and this Epicurious recipe I found online (and a few other versions I found online), I've got the basic idea, and now I'm trying to figure out my best version of it. For tonight's iteration, I used 1/4 of a bottle of prosecco that I got at Costco for $6.99. I saw the other day that Trader Joe's had prosecco for the same price.

I used heavy whipping cream and reduced the sauce, but I still wish I could make it thicker without having to add corn starch. I also think next time I'll make it with chicken thighs. I don't think that even bone-in split chicken breast can achieve the moistness and tenderness that thighs do.

ETA: My best friend from college reminds me that chicken in champagne cream sauce was served at her wedding reception, and as maid of honor, I was there and ought to remember, but that was who knows how many years ago!?!