Sauté mushrooms: Heat 1 tablespoon oil in a 12-inch heavy skillet over moderately high heat until hot but not smoking, then sauté one fourth of mushrooms with 1 tablespoon shallot, 1/2 teaspoon garlic, 1/2 tablespoon butter, 1/2 tablespoon thyme, 1/4 teaspoon kosher salt, and 1/8 teaspoon pepper, stirring, until mushrooms are browned and tender, about 3 minutes. Transfer to a shallow baking pan lined with paper towels (you want the flavor of the butter, but not the grease). Wipe out skillet. Sauté remaining mushrooms with seasoning in 3 batches in same manner, wiping out skillet between batches.
Make vinaigrette: Wash leek in a bowl of cold water, agitating water to loosen any grit, then lift out leek and drain in a sieve.
Heat 2 tablespoons oil in cleaned 12-inch skillet over moderately low heat until hot, then cook leek, celery, carrot, and remaining teaspoon kosher salt, stirring occasionally, until vegetables soften, about 10 minutes. Add whole garlic clove, bay leaf, and coriander seeds and cook, stirring occasionally, until vegetables are very tender, 8 to 10 minutes more. Stir in mushrooms, stock, vinegar, and bouquet garni and simmer 2 minutes. Remove from heat and stir in remaining 1/4 cup oil. Let stand 5 minutes. Discard bouquet garni, bay leaf, and garlic clove and season with salt and pepper, then transfer mixture to a colander set over a bowl and let drain 3 minutes. Reserve vinaigrette. (You will have about 3/4 cup.)
Bake crottins and assemble salad: Put oven rack in middle position and preheat oven to 350°F.
Arrange crottins in 1 layer in a 9-inch baking pan and spoon about half of reserved vinaigrette over them.
Bake crottins, basting with vinaigrette once or twice, until they are slightly softened and bubbling on the bottom, 10 to 15 minutes.
Toss salad greens with remaining vinaigrette to coat and divide among 8 salad plates. Cut crottins in half, then top salad greens with crottin halves and mushrooms.
*Available at Murray's Cheese Shop (888-692-4339; ).