Melt the butter with the olive oil in a large skillet over medium heat. Add the sliced onions with a pinch of salt and cook, stirring occasionally, for 45 to 50 minutes, until deeply caramelized. Lower the heat and add a splash of water if the onions start to stick. Stir in the minced garlic and cook for 3 to 5 more minutes.
2 large yellow onions, 2 tablespoons unsalted butter, 1 tablespoon extra virgin olive oil, 2 garlic cloves
Pour in the wine and use a wooden spoon to scrape up the browned bits from the bottom of the pan.
2 tablespoons dry white wine
Stir in the Worcestershire sauce and thyme, then cook for 2 more minutes, until the liquid has mostly evaporated. Remove the pan from the heat and let the onions cool completely. Important: never add warm onions to the yogurt, or the dip will turn thin and watery.
1 teaspoon Worcestershire sauce, 1 teaspoon fresh thyme leaves
In a medium bowl, whisk together the Greek yogurt, garlic powder, and black pepper.
½ teaspoon garlic powder, Kosher salt and black pepper, 2 cups full-fat Greek yogurt
Fold in the cooled onion mixture and taste before adding any salt. If the dip feels thicker than you like, whisk in a small splash of heavy cream.
Cover and refrigerate for at least 2 hours before serving, so the onions have time to soften into the yogurt and the flavors can fully develop.