Preheat the grill.
Bring a large pot of salted water to a boil. Prepare an ice bath. Trim away the bottom inch of the broccoli rabe stems. Blanch the broccoli rabe in the boiling water for 1 minute, then drain and plunge into the ice bath to cool. Drain again, pat dry, and cut into 1-inch pieces.
Meanwhile, in a small bowl, soak the sun-dried tomatoes in the boiling water for 10 minutes.
In a 10 to 12-inch saute pan, heat 3 tablespoons of the olive oil over medium-high heat until just smoking. Toss in the scallions and cook, stirring often, until just wilted, about 2 minutes. Add the broccoli rabe and vermouth and cook until the scallions are quite soft, 2 to 3 minutes. Season with salt and pepper. Set aside to cool to room temperature.
In a blender, combine the sun-dried tomatoes, with their soaking water, the vinegar, capers, and the remaining 1/4 cup olive oil and blend until smooth, about 1 minute. Set aside.
To clean the soft-shell crabs, cut off the eyes and mouth. Season with black pepper. Grill, turning once, until crisp and red, about 5 minutes on each side.
Divide the broccoli rabe mixture among 4 plates. Place 3 crabs on each plate, drip 2 tablespoons of the sun-dried tomato pesto around the crabs, and serve immediately.
Recipe courtesy of "Molto Italiano: Simple Italian Recipes for Cooking at Home" by Mario Batali, Harper Collins, 2005