1) 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 three minutes.
2) 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.
For the fish:
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 93°C. Reduce the heat to low to sustain the 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 250ml of 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.