How to Make It
Preheat the oven to 350°. Toss the shiitakes with 1 tablespoon of the olive oil. Spread them on a baking sheet and roast for about 20 minutes, turning once, until tender and barely crisp. Let cool.
In a blender or food processor, pulse the mushrooms and garlic until finely chopped. Add the lemon juice and, with the machine on, pour in the remaining olive oil in a thin stream. Transfer to a bowl. Stir in the truffle oil and season with salt and pepper.
Heat the vegetable oil in a saucepan. In a bowl, toss the shallots with the flour, shaking off the excess. Working in 2 batches, fry the shallots over high heat, stirring, until golden and crisp, about 6 minutes. Transfer the shallots to paper towels to drain. Season lightly with salt.
In a large bowl, toss the frisée with the radicchio and endives. Add half of the dressing and toss well. Season with salt and pepper, add the remaining dressing and toss again. Transfer the salad to a platter, top with the prosciutto and fried shallots and serve.