Preheat the oven to 400ºF.
Add the white onions to a baking sheet. Add 3 tablespoons of olive oil and 1 teaspoon of salt to the onions. Toss the onions until they are all coated in oil. Gather all of the onions to the middle of the pan so they are all in a pile. If they are spread out, they will burn.
Run the open end of the garlic under water so that the cloves become wet. Drizzle with 1 teaspoon of olive oil and then wrap the head of garlic in tin foil. Place it on the baking sheet.
Bake the onions for 40-50 minutes, tossing every 20 minutes until the onions are brown and caramelized.*
While the onions are baking add the Greek yogurt, sour cream, Worcestershire, fresh thyme, the remaining salt, and pepper to a bowl and mix to combine.
When the onions are caramelized, take a kitchen shears and cut through the onions so they are cut up into smaller pieces.
Add the onions to the yogurt mixture and squeeze the cloves out of the garlic head. Smash the cloves with the back of a spoon and stir all of the ingredients together to combine.
Enjoy immediately with crackers or crostini or cover and refrigerate. The dip will become more flavorful the longer it sits.