Place the onions in a heavy 3-quart (3-L) saucepan. Stir in the oil, cover, and cook over low heat about 10 minutes, until they are soft but have not taken on any color.
Stir in the carrots, celery, and potato, cook for about a minute, then add the stock, 1 1/4 cups (310 ml) of the wine, and the bay leaves.
Simmer, partly covered, for about 30 minutes, until the vegetables are very tender. Remove the bay leaves.
Allow the mixture to cool briefly, then puree in a blender or food processor.You may have to do this in 2 batches. Strain the soup.
To serve, reheat the soup and season it with salt and pepper.
Spoon it into 6 warm soup plates.
At the table, pour 1.5 to 2 tablespoons (20 to 30 ml) of chilled prosecco into each portion. The soup will froth up a bit.