In a large pot of boiling salted water, blanch the rapini for 3-4 minutes until tender. Drain and immediately transfer to an ice water bath to stop the cooking process.
In a pan, heat 2 tablespoons of olive oil over medium heat. Sauté minced garlic until fragrant.
Add the blanched rapini to the pan. Season with salt and pepper. Cook for an additional 3-4 minutes.
Transfer the rapini mixture to a blender or food processor. Add lemon zest and juice. Blend until smooth. Adjust seasoning if necessary. Keep warm.
Pat the scallops dry with paper towels. Season both sides with salt and black pepper.
In a skillet, heat 2 tablespoons of olive oil over medium-high heat. Place the scallops in the skillet, ensuring they are not too crowded. Cook for 2-3 minutes on each side or until they develop a golden-brown crust and are opaque in the center.
Spoon a generous portion of rapini purée onto each plate, arrange the seared scallops on top of the purée. Garnish with additional lemon zest and a squeeze of lemon juice and serve.
