Puree the oil, basil, pine nuts and spices in a measuring cup. Mix in the parmesan, lemon zest and juice. Cover the pesto and set aside.
Rinse the seabream (inside and out) in cold water, pat dry. Make diamond-shaped incisions (approx. 5 mm deep) on both sides of the fish without damaging the bones. Season the fish inside and out, brush with oil.
Grill the fish over/on a medium heat (approx. 200 °C for approx. 8 mins. on each side. Serve the sea bream together with the pesto.