In large saucepan or Dutch oven, heat 3 tablespoons oil over medium heat. Add onions and 1½ teaspoons thyme; salt and pepper to taste. Reduce heat to medium-low and cook onions, stirring frequently, until golden brown (about 20-25 minutes).
Add sherry or ½ cup broth, stirring and scraping pan until sherry is evaporated. Add broths; bring to a boil. Reduce heat; simmer 30 minutes, stirring occasionally. Stir in remaining thyme the last 10 minutes.
Meanwhile, lightly brush bread with remaining oil. Place on baking sheet; broil until golden brown (about 1-2 minutes).
Ladle soup into 8 ovenproof soup crocks or bowls; place on a baking sheet. Top each crock with bread and cheeses. Broil until cheese is browned and bubbly.
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