Dice the onions OR cut them into strips if you prefer. (I have tried both ways and prefer to dice the onion. Otherwise, I end up with stringy onions hanging out of my mouth taking a bite - not too charming lol). *See notes for link to onion cutting tutorial.
Heat the butter in a large skillet over medium heat. (You could also use extra virgin olive oil or a combination of oil and butter). When the butter starts to foam, add the onion and turn down the heat to low.
Sprinkle a little salt to taste.
The key to perfectly caramelized onions is to cook them low and slow for the next 30-40 minutes. Stir the onions every so often, allowing for them to develop some golden color, but not burn. If the pan gets too dry, add a little water a tablespoon at a time to prevent the onions from burning. Adding water instead of more butter or oil keeps the onions from getting too greasy.
If desired add a little brown sugar to deepen the caramelization.
Once the onions are nice and caramelized, deglaze the pan with a splash of balsamic vinegar or red wine (the one that you'll be pairing with your lamb sliders, of course! 😉 ).
Set the onions aside until the sliders are ready to assemble.