Surprised there wasn't a thread already. We live just south of the river and so do s fair amount of eating in Pilsen and have been going to Yvolina's for some time. They've won Mole de Mayo, which we always attend for the ease of trying great mole.
I think they strike the best balance between tradition and updates, as their vegan offerings are equally popular. We also occasionally take home jars of mole; I'm especially fond of the orange almond one.
We also love our tamale lady in front of Cermak Produce on Halsted for regular tamales, but when we choose to be unfaithful to her and go Oaxacan, it is always Yvolina's. It's GNR material. One or two tricks it does very well, family-run, fantastic. In pre-Covid times, they would sell out and close up early, so be warned, but they're currently set up for carryout only and doing some decent business.