Thinly slice the onions. Heat a 6-quart stockpot. Add the oil and heat. Add the onions and saute until golden brown over medium-low heat, about 25 to 30 minutes. Deglaze the pan with port. Add stock, salt, pepper, and bouquet garni, and simmer for 30 to 40 minutes.
Preheat the broiler.
Pour the soup into 6 oven-proof bowls. Top each bowl with 2 slices of bread and sprinkle with the cheese. Brown under the broiler until the cheese is golden brown and bubbly.