Well, that went faster than I thought: the brand is Alchemade, and I have several copper products from them and they're all excellent quality.

Here are the mule mugs I have: https://www.amazon.co.uk/gp/product/B00GVJTCXA/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

Edit: here's the Amazon US link: https://www.amazon.com/Alchemade-Copper-Barrel-Moscow-Mules/dp/B00L9JKUDS/ref=sr_1_7?crid=1Y122EOSXW3CJ&dchild=1&keywords=alchemade+copper+mug&qid=1600757481&sprefix=alchemise%2Caps%2C255&sr=8-7