Add oil to a sauté pan and turn the heat to medium-high (9 out of 14 on my stove).
Add the onions and garlic to the pan and let them cook for a few minutes. They should become soft without coloring.
Add sugar, vinegar, and balsamic and stir well.
Turn down the heat and let it simmer for 15 minutes.
Season with salt and pepper and add mustard and honey to the pan. Turn up the heat slightly and let it cook for about 5 more minutes, allowing the liquid to coat/stick to the onions.
Taste and adjust with more salt and pepper if needed, and they are ready to serve.