Peel and halve onions through root end and slice into 1/4" - 1/8" thick slices, using the onions natural grain to make strips for you.

Heat 2 Tbsp. butter or oil in a large flat-bottomed heavy pan on medium heat. 

Note: The video in the post shows a saucepan, but a larger, heavy pan is much preferred. Using a wide base gives water room to evaporate, allowing onions to caramelize rather than steam.

Add onions to the pan and stir. Then season with a pinch of salt and pepper. Let the onions begin to soften and turn translucent.

Reduce heat to medium-low and continue to cook onions, stirring often to prevent them from getting too much color in one place or sticking.

 If onions stick or get too brown in one place, reduce heat.

If you see bare, browned spots in the pan, add a bit of cooking liquid and stir. The liquid will help scrape the cooked-on bits and will season the onions. 

Once the onions began to take on a caramel color, keep a close eye on them. For extra-dark onions, this is when you add balsamic. 

This is the point when your onions need constant attention. Keep stirring until they are the desired color. I like mine a caramel color with a few dark edges.

Let onions cool, then transfer to an airtight container OR you can do what I do and eat them right from the pan! 

Chill any leftover onions. They will keep up to one week and can be eaten warmed or chilled right from the refrigerator. They also freeze well!