1. In a heavy 2- to 3-quart saucepan, melt the butter over moderate heat. Add the onions, carrots, potatoes, cauliflower and celery root. Stirring frequently, cook for about 5 minutes, then pour in the stock.
2. Bring to a boil over high heat, partially cover the pan, and lower the heat. Simmer for 20 minutes, or until the vegetables are tender but not too soft.
2. Meanwhile, in a heavy 12-inch skillet, fry the bacon over moderate heat until the slices are brown and crisp around the edges and have rendered most of their fat.
2. With tongs, transfer the bacon slices to paper towels to drain. Add the slices of bread to the fat remaining in the skillet and fry until they are crisp and brown on both sides. Set the fried bread aside on paper towels to drain.
3. Just before serving, preheat the broiler to its highest setting. Pour the soup into a ½- to 2-quart ovenproof tureen or casserole.
2. Float the bacon slices on top of the soup and cover each of them with a slice of fried bread and then a slice of cheese, arranging them so they mask the surface of the soup.
2. Slide the tureen or casserole under the broiler (the top of the tureen should be about 3 inches from the heat) and broil for 2 or 3 minutes, until the cheese melts and turns a delicate brown.
