Pat the tofu slices dry with paper towels. Brush the tofu and bread on both sides with the remaining 2 tablespoons of olive oil and season with salt and pepper. Grill the bread over moderately high heat, turning once, until lightly charred, about 2 minutes. Grill the tofu, turning once, until grill marks form and the tofu is heated through, about 6 minutes. Transfer the grilled bread and tofu pieces to plates. Spoon the piquillo salsa verde over the tofu and serve.