Cut the onion into very thin slices. Place the butter and oil in a pan and heat. Add the onion and cover, letting it cook for about 10 to 12 minutes.
Uncap and increase the heat. Add the pinch of sugar and keep stirring until the onion caramelizes and gains a brownish tone. Sprinkle with flour and stir continuously for 3 minutes.
Add the vegetable broth that should be very hot, the wine and the soy sauce and let it boil for another 10 to 15 minutes, over low heat. Rectify with salt.
Meanwhile put the bread slices in the oven, sprinkled with the grated cheese of the island and let it melt and the bread is golden brown.
Serve the soup with the slices of bread and if you want, sprinkle with more cheese.