Heat a grill. Cut the shells of the scampi and grill them for 2 minutes on each side. Deglaze with the cognac.

In a small bowl, combine parsley, garlic, olive oil, salt, and pepper. Blend with an immersion blender (for best color, chill the blender blades in the freezer first). Add more olive oil until you have an emulsion.

Serve the scampi topped with the green sauce and garnish with lemon and parsley.