Cut the bulbs from the fennel tops. Reserve two packed cups of fronds and chopped tender portions of the tops, and set aside.
Core and very thinly slice two of the fennel bulbs. Keep them in ice water while you prepare the rest of the salad. Core and slice the remaining bulb into pieces about six millimeters thick. Place on a baking sheet with one tablespoon of the olive oil, and season with salt and pepper. Roast, stirring occasionally, until tender and golden, about 20 minutes.
Meanwhile, bring a medium saucepan of salted water to a boil. Add the reserved fennel tops and fronds, and blanch until bright green and tender, about three minutes. Shock in an ice bath, and pat dry. Put in a blender with one tablespoon of the oil and two tablespoons water. Blend to make a smooth purée, adding a little more water if necessary. Season with salt and pepper.
To assemble the salad, whisk two tablespoons of lemon juice with the remaining three tablespoons of olive oil in a large bowl. Season with salt and pepper. Add up to one more tablespoon lemon juice, to taste. Thinly slice the Asian pears, and add them to the bowl. Drain the uncooked fennel, pat very dry, and add to the bowl. Season with salt and pepper, and toss well.
To serve, spread four serving plates with the fennel purée. Top with the roasted fennel, and then mound the salad on top of that. Finely grate pecorino over each serving, sprinkle with pistachios, and grind black pepper over all. Serve immediately.