Remove florets from broccoli rabe and cut stems and leaves into 1-inch pieces. In a 10-inch to 12-inch saute pan, heat 3 tablespoons extra virgin olive oil until just smoking. Toss scallions and cook 2 minutes, stirring often until just wilted. Add broccoli rabe and sweet vermouth and continue cooking 2 to 3 minutes, until scallions are quite soft. Season with salt and pepper. Set aside and allow to cool to room temperature. In a blender, add sundried tomatoes, soaking water, balsamic vinegar, capers and 1/4 cup extra virgin olive oil and blend until smooth, about 1 minute. Remove from blender and set aside.
Clean soft shell crabs by snipping off face and removing the skirt. Season with black pepper and place onto grill. Cook until crisp and bright red (about 5 minutes each side). Meanwhile, divide rabe/scallion mixture among 4 plates. Place 3 crabs on each plate, drip 2 tablespoons tomato pesto around crabs and serve immediately.