Bring a small pot of salted water to a boil over high heat. Add the broccoli rabe and cook until tender, about 5 minutes. Transfer the cooked broccoli rabe to an ice bath and let cool, about 3 minutes. Shake off the excess water and transfer to a food processor. Add the garlic, walnuts, honey, salt, and pepper process until smooth. With the machine running gradually pour in the extra-virgin olive oil. Transfer the pesto to a small bowl and stir in the Parmesan. Cover and set aside.
In a medium, heavy skillet, heat the olive oil and vegetable oil over medium-low heat. Using a deep-fry thermometer, heat the oil to 200 degrees F. Reduce the heat to low to sustain the 200 degree F temperature. Season the fish with salt and pepper. Gently place the fish in the oil making sure it is submerged beneath the surface. Poach the fish until just cooked through, about 6 to 7 minutes.
Place about 1/2 cup of Broccoli Rabe Pesto on a serving plate and gently smooth out to make a bed for the fish. Using a slotted fish spatula gently transfer the cooked fish from the poaching oil to the serving plate, placing the fish on top of the bed of pesto. Serve immediately.