In large saucepan or Dutch oven, heat oil over medium heat. Add onions and 1 teaspoon thyme; salt and pepper to taste. Reduce heat to medium-low and cook onions, stirring frequently, until golden brown (about 15 minutes).
Add sherry or ¼ cup chicken broth, stirring and scraping pan until evaporated. Add broths and remaining thyme; increase heat to medium-high and bring soup to a boil. Reduce heat and simmer 10 minutes, stirring occasionally.
Ladle soup into 4 ovenproof soup crocks or bowls; top each bowl with croutons and cheeses. Place bowls on baking sheet and broil until cheese is browned and bubbly.