Preheat the oven to 400ºF.
Spread the sliced onions onto baking sheet and place the head of garlic cut-side down onto the baking sheet. Drizzle with olive oil, season with sugar and salt, and toss to combine.
Bake for 15 minutes.
Remove the pan from the oven and use a spatula to make an onion pile (scoot all of the onions together). Flip over the head of garlic.
Place back into the oven and bake for another 15 minutes. After 15 minutes, toss again. If the onions have reduced in size and turned a dark golden brown/dark purple color, you know they are done. If the onions are still plump and light in color, they need to continue cooking.
Once the onions have caramelized, transfer the onions and head of garlic to a cool baking sheet or plate. Set aside to cool.
After the head of garlic is cool enough to handle, use your hands to squeeze out the cloves into a large bowl. Use a fork to mash the roasted garlic into a paste.
Add the Greek yogurt, sour cream, and Worcestershire sauce to the bowl. Mix well.
Use a pair of kitchen scissors to cut the caramelized onions into smaller, bite-sized pieces and transfer into the large bowl.
Mix the onions with the rest of the dip and taste test. Add additional salt/pepper if needed.
Garnish with fresh thyme and serve with your favorite crackers, pretzels, veggies, breads, bagels, and more!