Set oven rack at lowest level, preheat to 450 degrees. Combine onions, shallots, garlic and oil in large shallow roasting pan. Roast for 20 to 30 minutes, stirring every 5 minutes, or until onions are golden brown. Remove from onion and pour in 1 cup of chicken broth. Stir liquid in pan, scraping the bottom to loosen and dissolve caramelized bits. Transfer the onion mixture to a soup pot and add brandy, thyme and remaining broth. Bring to a boil, reduce heat to low and simmer, covered, for 30 minutes. Season to taste with salt and pepper. Serve topped with parmesan and perhaps some toasted french bread.