To make the confit: Stem and clean the mushrooms, leaving the caps whole, except the portobellos, which can be quartered. In a colander, combine the mushrooms and sprinkle generously with kosher salt and freshly ground black pepper. Set the colander aside in a bowl, for 30 minutes to 1 hour, stirring occasionally, allowing the mushrooms to release as much liquid as possible (do not reserve the liquid). Pat the mushrooms dry with a paper towel.
Preheat oven to 225 degrees F.
In a large baking dish, combine the mushrooms with the oil, garlic, bay leaves, thyme, rosemary, and black pepper. Cover with foil, and bake for 1 1/2 hours, until the mushrooms are very tender. Transfer the mushrooms to a strainer or colander set over a medium bowl to catch the oil. Remove and discard the bay leaves, thyme, and rosemary. Reserve 1/2 cup of the oil, and save the rest of the mushroom oil for other recipes.
To make the salad: In a small bowl, combine the garlic, vinegar, mustard, salt, and season with salt and pepper, to taste. Gradually whisk in the 1/2 cup of reserved mushroom oil to make a creamy dressing.
In a medium bowl combine the mushrooms, barley, radish, carrots, green onions, and parsley; lightly toss with a little of the dressing. Season with salt and pepper, to taste.
In another medium bowl, toss the mesclun with a little of the dressing and season with salt and pepper, to taste. Reserve the remaining dressing for another use.
To serve, divide the greens among 4 plates. Top with the mushroom salad and drizzle with truffle oil. Top with the carrot curls and serve immediately.
With a Japanese-style rotary cutter cut the carrots into long curls.
Pour the oil into a heavy-bottomed pot to a depth of 2 inches. Heat over medium-high until the oil registers 360 degrees on a deep-fry thermometer.
In a medium bowl, toss the carrots with the instant flour to coat evenly, and shake off the excess. Fry the carrot curls, in batches if needed, until crisp and very lightly browned. Remove from the oil with a slotted spoon and drain on a paper towel-lined plate. Season with salt, to taste, and serve.
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