1. Place the onions, olive oil and sugar into a large skillet. Stir until the onions are covered.
2. Place the skillet over medium-low heat. Slowly cook the onions, stirring occasionally. The onions will soften and slowly brown as they cook, and should take about an hour to completely caramelize.
3. Raise the heat to medium and add the garlic and thyme. Cook everything for about 1 minute, continuously stirring..
4. Stir in the balsamic vinegar and continue cooking and stirring everything for about 1 minute, until most of the liquid dries up. Remove the skillet from heat and let the onions cool a bit.
5. While the onions cool, place the cashews into a food processor bowl with the milk. Blend to a smooth paste.
6. Add the tofu, lemon juice, Worcestershire sauce, and onion powder. Blend again until the mixture is smooth.
7. Add the onions to the food processor. Blend again until the onions are finely chopped and incorporated into the dip.
8. Season the dip (generously) with salt and pepper to taste, and blend the mixture one final time.
9. Spoon the dip into a bowl and top it with fresh chives.