In a small saucepan, add 2 cups of cider and bring to a boil. Continue to cook over high heat until the cider is reduced to 1/3 cup, about 20 minutes.
PREPARE THE SOUP:
Peel the onions and cut them in half through the root end. Place the flat end on a cutting board. Cut into very thin slices, less than 1/8-inch thick.
In a large, heavy pot, heat the butter and oil until the butter is melted. Add the onions and cook over medium-high heat, stirring frequently, until they soften and get very dark brown (some will blacken), about 20 minutes. Add the broth and cider and bring to a rapid boil.
Lower the heat and add 5 long thyme sprigs, sugar, salt and freshly ground black pepper to taste. Cook, covered, for 30 minutes over medium heat, stirring often.
Remove the thyme sprigs from the soup and pull the soup off the heat and let it cool down a bit. Then transfer the soup to the bowl of a food processor. Be careful not to fill the bowl of the processor too full. Super hot soup may splash out of the processor, so be careful! Process until very smooth; this should take several minutes since you're processing onions! Add salt and pepper to taste and transfer the soup to 6 soup bowls. Drizzle each with some of the cider syrup and garnish with fresh thyme leaves and a sprinkling of cheese.
*Be sure to use fresh, unpasteurized apple cider from the refrigerated case in the supermarket.
*If you are preparing this recipe as gluten-free, just be sure to use a brand of beef broth that is know to be free of gluten.