Preheat oven to 325 degrees Fahrenheit. Drizzle whole onions with one teaspoon olive oil in a baking pan, and drizzle garlic cloves with one teaspoon oil in another baking pan.

Roast until tender, about 30 minutes for garlic and an hour and a half for onions. Let cool. Squeeze garlic out of skin and mash. Peel onions and slice.

Heat remaining two tablespoons olive oil in a large, heavy saucepan over medium heat. Add onions and sauté for 15 minutes. Stir in garlic.

Add chicken stock and thyme, and bring to a boil. Reduce heat and simmer for 15 minutes.

Add potatoes and simmer until tender, about 15 minutes. Let cool, then remove thyme sprigs.

Purée until smooth. Reheat and serve with croutons.