Peel the onions. Cut in half lengthwise. Then slice lengthwise into thin uniform pieces.
Heat the butter and oil in a 12.5” skillet over medium-high heat. Add the onions and stir to coat. Cook tossing often with tongs, until hot and sizzling, about 4 to 5 minutes.
Add a pinch of salt (which helps draw out moisture) and toss to combine.
Cover, reduce heat to medium-low, and cook until onions have shrunk in half, about 8 to 10 minutes.
Remove the cover and stir the onions with a wooden spoon, scraping the bottom of the pan to avoid sticking and burning. Reducing heat as required to maintain a gentle simmer, until liquid has evaporated, about 20 minutes.
As the pan dries, increase heat to medium and scrape the bottom and sides of the pan with a wooden spoon, pulling the onions away from the sides of the pan to prevent burnt bits around the sides.
Add a couple of tablespoons of water and a teaspoon of sugar and stir, scraping the browned bits on the bottom of the pan.
Continue to cook, scrape, cook some more and scrape, splashing in additional water, as required, until the onions are a rich, brown color. 20 to 30 minutes. Remove the onions from the pan and cool.