Prepare the onions: Heat butter and olive oil in a large skillet over medium heat until melted and hot. Add the thinly sliced onions and toss to coat evenly with the fats. Spread them out in an even layer.
Begin the caramelization process: Cook onions for 5 minutes undisturbed, then stir and reduce heat to medium-low. Continue cooking, stirring every 5-7 minutes, for about 25-30 minutes. The onions should slowly turn golden brown, not burn.
Add the sugar: Once the onions have softened and begun to brown, sprinkle the sugar over them and stir to incorporate. This will help accelerate the caramelization.
Deglaze the pan: When the onions are deeply golden and jammy (about 10 more minutes), add the balsamic vinegar and stir, scraping up any browned bits from the bottom of the pan. Cook for 2-3 minutes until the vinegar is absorbed.
Season the onions: Remove from heat, stir in the thyme leaves, and let cool for 15 minutes.
Preheat the oven to 375°F (190°C).
Make the cheese base: In a large mixing bowl, combine the softened cream cheese, sour cream, and mayonnaise until smooth. Add the minced garlic, Worcestershire sauce, salt, and pepper, mixing well.
Combine everything: Fold in the cooled caramelized onions and 6 oz of the grated Gruyère (reserve the remaining 2 oz for topping).
Prepare for baking: Transfer the mixture to a 1-quart baking dish. Sprinkle the remaining Gruyère on top.
Bake the dip: Place in the preheated oven and bake for 15-20 minutes until bubbly and golden brown on top.
Serve properly: Let rest for 5 minutes before serving with crusty bread, crackers, or fresh vegetables.