In a large nonstick frying pan, heat 3 tablespoons of the olive oil over moderate heat.
Add the cubed bread, 1/2 teaspoon salt, and 1/4 teaspoon pepper and stir to coat the bread with the oil. Saut the bread until crisp and lightly browned, about 5 minutes.
Remove from the heat and stir in half the garlic.
Transfer to a large salad bowl.
In the same pan, heat the cooking oil over moderately high heat.
Add the mushrooms, 1/4 teaspoon pepper, and the remaining 1/4 teaspoon salt. Cook, stirring frequently, until the mushrooms are tender, 2 to 3 minutes.
Add half the remaining garlic and the parsley and cook, stirring, for 1 minute longer.
Add the mushrooms to the croutons.
Put the eggs, vinegar, anchovy paste, and the remaining garlic, 1/4 teaspoon pepper, and 5 tablespoons olive oil in a blender or food processor and whir until smooth.
Add the lettuce to the mushrooms and croutons, sprinkle with Parmesan, and then add the dressing. Toss to coat.
Wine Recommendation: Because sparkling wines have surprisingly high acidity,a nonvintage brut Champagne will go well with this salad, matching the vinegar in the dressing and cutting the Parmesan's richness.