Heat oil in a Dutch oven set over medium heat. Add onion and cook, stirring frequently, for 30 minutes or until caramelized. Add garlic and cook for 30 seconds. Stir in maple syrup.
Add the broth and half of thyme; bring to a boil. Reduce heat and simmer for 20 minutes. Season to taste with salt and pepper. Preheat broiler.
Divide soup between 6 ovenproof bowls. Top with toast slices and equal amounts of cheese. Broil for 2 to 3 minutes or until cheese melts and lightly browns. Garnish with remaining thyme and serve.