Bring water to a boil in a medium saucepan. Add pearl onions and boil 3 minutes. Drain and rinse in cold water. Peel onions.
In the same pan, add butter over medium heat. When butter is melted, stir in 3/4 teaspoon sugar. Add the onions and cook until golden brown, stirring often.
Add chicken broth, bay leaf, thyme, salt, pepper and then remaining sugar. Mix well. Add carrots and carefully mix again, taking care not to break up the onions.
Bring to a boil, then reduce heat, cover and simmer for about 6 minutes or until carrots are tender.
Remove from heat and take out bay leaf. Serve with a slotted spoon.