Transfer to a skillet along with butter and oil. Add the black pepper powder.
Cook on medium heat and continue stirring. Add balsamic vinegar and a little bit of brown sugar (optional, to speed up caramelization) and turn down the heat.
Cook until the onions have developed a deep golden brown color, then add the thyme and take off heat.
Notes
Slice the onions thinly and evenly so they soften and cook at the same rate.
Use a wide, heavy-bottomed skillet to allow the onions to cook evenly without overcrowding.
Cook over medium heat initially, then reduce the heat once the onions begin to soften and brown.
Stir frequently, especially toward the end of cooking, to prevent the onions from sticking or burning.
Add a splash of water if the skillet becomes too dry before the onions are fully caramelized.
Adjust the balsamic vinegar to taste, or add a pinch of brown sugar for a slightly sweeter finish.
Swap white onions for yellow or sweet onions, or replace thyme with rosemary for a different flavor.
Serve over burgers, grilled cheese sandwiches, steak, pizza, or mashed potatoes.
Store leftovers in an airtight container in the refrigerator for up to 4 days, or freeze in small portions for longer storage.