Paul Bocuse's onion soup

Thinly slice one and a half pounds, about 600 grams, of yellow onions.

Melt one and a half sticks of butter in a skillet, add the onions and saute until nicely coloured but not too brown; about 36 minutes on medium heat.

Add two tablespoons of flour, tilting the pan and stirring it into the onions as if making a roux, about two minutes.

Take off the heat and add the onions to a Dutch oven holding ten and a half cups of water.

Salt, crack in pepper and add a bouquet garni of a thyme sprig, the green of a leek, a celery stalk with leaves and one bay leaf.

Simmer about 30 minutes.

Remove the bouquet garni, then pass the soup through a food mill with a medium plate, processing the onions through into the broth.

Season again with salt and freshly cracked pepper.

Finely slice half a baguette, then cut the slices into sticks.

Dry the bread sticks in a 325 degree Fahrenheit oven until dried out.

Line the bottom of the bowl with the bread sticks, half a handful of cheese in between them and the remaining handful on top; ladle in the soup so the sticks rise.

Separately whisk one egg yolk with a tablespoon of Madeira wine and keep it aside.

Place the bowl under a preheated broiler on high until the cheese melts and bubbles, about two minutes.

At the table, stir the egg yolk and Madeira mixture into the soup, about a quarter of the mixture per bowl.