Place the shallot into a small bowl and sprinkle with sugar and a large pinch of salt. Add the mustards and slowly stir in the vinegar. Slowly pour in the oil whisking constantly. Season and set aside.
For the Salad
Heat the oil in a medium sized, heavy-bottomed frying pan. Sauté the mushrooms for two to three minutes on both sides then remove to a piece of kitchen paper. Season well and allow to cool.
Place the potatoes in a pan of cold salted water. Bring to the boil and cook for ten to fifteen minutes or until cook. Plunge the potatoes into iced cold water to arrest the cooking process.
Bring another pan of salted water to the boil and add the French beans, cook for four to five minutes, and then plunge into iced water like the potatoes.
Half fill a medium sized pan with water, enough to generously cover your eggs, and bring to a simmer. Carefully lower the eggs into the gently boiling water with a spoon and start your timer. Cook for six minutes and plunge into iced cold water. When totally chilled peel, halve and set aside.
Break up the lettuce then arrange the ingredients in four bowls, dress and serve.