Place 1 onion half on a cutting board so root end is facing you, then thinly slice lengthwise (¼"–⅛" thick), starting at one side and working all the way to the other (your knife will run through root halfway through; you are not starting or ending at root end). Reduce heat to medium-low and continue to cook onions, stirring every few minutes and reducing heat a little if sticking or getting too brown in any one place, until blond, 15–20 minutes more. For onions that are both softer and more caramelized (for a patty melt or onion dip), continue to cook, stirring often and adding a splash of low-sodium chicken broth or water if the bottom of pan starts to burn, until unmistakably golden brown, 15–20 minutes more.