1. In a blender, puree the silken tofu with the olive oil, lemon juice, the 1 1/2 tablespoons of Parmigiano, the anchovy, garlic, Worcestershire and mustard; season the dressing with salt and pepper.
2. Wrap the firm tofu in paper towels and press out some of the water. In a large skillet, heat 1/4 inch of vegetable oil until shimmering. In a bowl, toss the tofu with the cornstarch until coated. Add the cubes to the oil and fry over moderately high heat, turning once, until crisp, about 8 minutes. Using a slotted spoon, transfer the croutons to a paper towellined plate; season with salt.
3. In a large bowl, toss the romaine with the dressing and two-thirds of the croutons. Transfer the salad to plates and top with the remaining croutons. Sprinkle with Parmigiano and serve.